Daily Papers

We investigate a variational method for ill-posed problems, named graphLa+Psi, which embeds a graph Laplacian operator in the regularization term. The novelty of this method lies in constructing the graph Laplacian based on a preliminary approximation of the solution, which is obtained using any existing reconstruction method Psi from the literature. As a result, the regularization term is both dependent on and adaptive to the observed data and noise. We demonstrate that graphLa+Psi is a regularization method and rigorously establish both its convergence and stability properties. We present selected numerical experiments in 2D computerized tomography, wherein we integrate the graphLa+Psi method with various reconstruction techniques Psi, including Filter Back Projection (graphLa+FBP), standard Tikhonov (graphLa+Tik), Total Variation (graphLa+TV), and a trained deep neural network (graphLa+Net). The graphLa+Psi approach significantly enhances the quality of the approximated solutions for each method Psi. Notably, graphLa+Net is outperforming, offering a robust and stable application of deep neural networks in solving inverse problems.

Sparse Autoencoders (SAEs) have emerged as a promising approach for interpreting neural network representations by learning sparse, human-interpretable features from dense activations. We investigate whether incorporating variational methods into SAE architectures can improve feature organization and interpretability. We introduce the Variational Sparse Autoencoder (vSAE), which replaces deterministic ReLU gating with stochastic sampling from learned Gaussian posteriors and incorporates KL divergence regularization toward a standard normal prior. Our hypothesis is that this probabilistic sampling creates dispersive pressure, causing features to organize more coherently in the latent space while avoiding overlap. We evaluate a TopK vSAE against a standard TopK SAE on Pythia-70M transformer residual stream activations using comprehensive benchmarks including SAE Bench, individual feature interpretability analysis, and global latent space visualization through t-SNE. The vSAE underperforms standard SAE across core evaluation metrics, though excels at feature independence and ablation metrics. The KL divergence term creates excessive regularization pressure that substantially reduces the fraction of living features, leading to observed performance degradation. While vSAE features demonstrate improved robustness, they exhibit many more dead features than baseline. Our findings suggest that naive application of variational methods to SAEs does not improve feature organization or interpretability.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

Out-of-distribution (OOD) detection is critical to building reliable machine learning systems in the open world. Researchers have proposed various strategies to reduce model overconfidence on OOD data. Among them, ReAct is a typical and effective technique to deal with model overconfidence, which truncates high activations to increase the gap between in-distribution and OOD. Despite its promising results, is this technique the best choice for widening the gap? To answer this question, we leverage the variational method to find the optimal operation and verify the necessity of suppressing abnormally low and high activations and amplifying intermediate activations in OOD detection, rather than focusing only on high activations like ReAct. This motivates us to propose a novel technique called ``Variational Rectified Activation (VRA)'', which simulates these suppression and amplification operations using piecewise functions. Experimental results on multiple benchmark datasets demonstrate that our method outperforms existing post-hoc strategies. Meanwhile, VRA is compatible with different scoring functions and network architectures. \textcolor[rgb]{0.93,0.0,0.47}{Our code can be found in Supplementary Material}.

Recent work has explored sequence-to-sequence latent variable models for expressive speech synthesis (supporting control and transfer of prosody and style), but has not presented a coherent framework for understanding the trade-offs between the competing methods. In this paper, we propose embedding capacity (the amount of information the embedding contains about the data) as a unified method of analyzing the behavior of latent variable models of speech, comparing existing heuristic (non-variational) methods to variational methods that are able to explicitly constrain capacity using an upper bound on representational mutual information. In our proposed model (Capacitron), we show that by adding conditional dependencies to the variational posterior such that it matches the form of the true posterior, the same model can be used for high-precision prosody transfer, text-agnostic style transfer, and generation of natural-sounding prior samples. For multi-speaker models, Capacitron is able to preserve target speaker identity during inter-speaker prosody transfer and when drawing samples from the latent prior. Lastly, we introduce a method for decomposing embedding capacity hierarchically across two sets of latents, allowing a portion of the latent variability to be specified and the remaining variability sampled from a learned prior. Audio examples are available on the web.

When training large flexible models, practitioners often rely on grid search to select hyperparameters that control over-fitting. This grid search has several disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the available data for training, and requires users to specify candidate values. In this paper, we propose an alternative: directly learning regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior. Our proposed technique overcomes all three disadvantages of grid search. In a case study on transfer learning of image classifiers, we show how our method reduces the 88+ hour grid search of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.

Knowledge-grounded conversation (KGC) shows great potential in building an engaging and knowledgeable chatbot, and knowledge selection is a key ingredient in it. However, previous methods for knowledge selection only concentrate on the relevance between knowledge and dialogue context, ignoring the fact that age, hobby, education and life experience of an interlocutor have a major effect on his or her personal preference over external knowledge. Without taking the personalization issue into account, it is difficult to select the proper knowledge and generate persona-consistent responses. In this work, we introduce personal memory into knowledge selection in KGC to address the personalization issue. We propose a variational method to model the underlying relationship between one's personal memory and his or her selection of knowledge, and devise a learning scheme in which the forward mapping from personal memory to knowledge and its inverse mapping is included in a closed loop so that they could teach each other. Experiment results show that our method outperforms existing KGC methods significantly on both automatic evaluation and human evaluation.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

This article deals with the following fractional (p,q)-Choquard equation with exponential growth of the form: $varepsilon^{ps}(-Delta)_{p}^{s}u+varepsilon^{qs}(-Delta)_q^su+ Z(x)(|u|^{p-2}u+|u|^{q-2}u)=varepsilon^{mu-N}[|x|^{-mu}*F(u)]f(u) in R^N, where s\in (0,1), \varepsilon>0 is a parameter, 2\leq p=N{s}<q, and 0<\mu<N. The nonlinear function f has an exponential growth at infinity and the continuous potential function Z satisfies suitable natural conditions. With the help of the Ljusternik-Schnirelmann category theory and variational methods, the multiplicity and concentration of positive solutions are obtained for \varepsilon>0$ small enough. In a certain sense, we generalize some previously known results.

Inspired by recent work in machine translation and object detection, we introduce an attention based model that automatically learns to describe the content of images. We describe how we can train this model in a deterministic manner using standard backpropagation techniques and stochastically by maximizing a variational lower bound. We also show through visualization how the model is able to automatically learn to fix its gaze on salient objects while generating the corresponding words in the output sequence. We validate the use of attention with state-of-the-art performance on three benchmark datasets: Flickr8k, Flickr30k and MS COCO.

Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent representations, a fundamental strength of variational methods, but also constrains the overall design space. To address these limitations, we propose Discrete Markov Bridge, a novel framework specifically designed for discrete representation learning. Our approach is built upon two key components: Matrix Learning and Score Learning. We conduct a rigorous theoretical analysis, establishing formal performance guarantees for Matrix Learning and proving the convergence of the overall framework. Furthermore, we analyze the space complexity of our method, addressing practical constraints identified in prior studies. Extensive empirical evaluations validate the effectiveness of the proposed Discrete Markov Bridge, which achieves an Evidence Lower Bound (ELBO) of 1.38 on the Text8 dataset, outperforming established baselines. Moreover, the proposed model demonstrates competitive performance on the CIFAR-10 dataset, achieving results comparable to those obtained by image-specific generation approaches.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

The FlowNet demonstrated that optical flow estimation can be cast as a learning problem. However, the state of the art with regard to the quality of the flow has still been defined by traditional methods. Particularly on small displacements and real-world data, FlowNet cannot compete with variational methods. In this paper, we advance the concept of end-to-end learning of optical flow and make it work really well. The large improvements in quality and speed are caused by three major contributions: first, we focus on the training data and show that the schedule of presenting data during training is very important. Second, we develop a stacked architecture that includes warping of the second image with intermediate optical flow. Third, we elaborate on small displacements by introducing a sub-network specializing on small motions. FlowNet 2.0 is only marginally slower than the original FlowNet but decreases the estimation error by more than 50%. It performs on par with state-of-the-art methods, while running at interactive frame rates. Moreover, we present faster variants that allow optical flow computation at up to 140fps with accuracy matching the original FlowNet.

Large language models often produce plausible but incorrect outputs. Existing heuristics such as HallBayes lack formal guarantees. We develop the first comprehensive theory of information-lift certificates under selective classification. Our contributions are: (i) a PAC-Bayes sub-gamma analysis extending beyond standard Bernstein bounds; (ii) explicit skeleton sensitivity theorems quantifying robustness to misspecification; (iii) failure-mode guarantees under assumption violations; and (iv) a principled variational method for skeleton construction. Across six datasets and multiple model families, we validate assumptions empirically, reduce abstention by 12--15\% at the same risk, and maintain runtime overhead below 20\% (further reduced via batching).

The capability to generate responses with diversity and faithfulness using factual knowledge is paramount for creating a human-like, trustworthy dialogue system. Common strategies either adopt a two-step paradigm, which optimizes knowledge selection and response generation separately, and may overlook the inherent correlation between these two tasks, or leverage conditional variational method to jointly optimize knowledge selection and response generation by employing an inference network. In this paper, we present an end-to-end learning framework, termed Sequential Posterior Inference (SPI), capable of selecting knowledge and generating dialogues by approximately sampling from the posterior distribution. Unlike other methods, SPI does not require the inference network or assume a simple geometry of the posterior distribution. This straightforward and intuitive inference procedure of SPI directly queries the response generation model, allowing for accurate knowledge selection and generation of faithful responses. In addition to modeling contributions, our experimental results on two common dialogue datasets (Wizard of Wikipedia and Holl-E) demonstrate that SPI outperforms previous strong baselines according to both automatic and human evaluation metrics.

The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere-ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air-sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the problem, which would allow for the usage of preexisting codes for the air and sea domain separately, as "black boxes". This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.

We focus on grounding (i.e., localizing or linking) referring expressions in images, e.g., "largest elephant standing behind baby elephant". This is a general yet challenging vision-language task since it does not only require the localization of objects, but also the multimodal comprehension of context --- visual attributes (e.g., "largest", "baby") and relationships (e.g., "behind") that help to distinguish the referent from other objects, especially those of the same category. Due to the exponential complexity involved in modeling the context associated with multiple image regions, existing work oversimplifies this task to pairwise region modeling by multiple instance learning. In this paper, we propose a variational Bayesian method, called Variational Context, to solve the problem of complex context modeling in referring expression grounding. Our model exploits the reciprocal relation between the referent and context, i.e., either of them influences the estimation of the posterior distribution of the other, and thereby the search space of context can be greatly reduced, resulting in better localization of referent. We develop a novel cue-specific language-vision embedding network that learns this reciprocity model end-to-end. We also extend the model to the unsupervised setting where no annotation for the referent is available. Extensive experiments on various benchmarks show consistent improvement over state-of-the-art methods in both supervised and unsupervised settings.

Often, labeling large amount of data is challenging due to high labeling cost limiting the application domain of deep learning techniques. Active learning (AL) tackles this by querying the most informative samples to be annotated among unlabeled pool. Two promising directions for AL that have been recently explored are task-agnostic approach to select data points that are far from the current labeled pool and task-aware approach that relies on the perspective of task model. Unfortunately, the former does not exploit structures from tasks and the latter does not seem to well-utilize overall data distribution. Here, we propose task-aware variational adversarial AL (TA-VAAL) that modifies task-agnostic VAAL, that considered data distribution of both label and unlabeled pools, by relaxing task learning loss prediction to ranking loss prediction and by using ranking conditional generative adversarial network to embed normalized ranking loss information on VAAL. Our proposed TA-VAAL outperforms state-of-the-arts on various benchmark datasets for classifications with balanced / imbalanced labels as well as semantic segmentation and its task-aware and task-agnostic AL properties were confirmed with our in-depth analyses.

We introduce a deterministic variational formulation for training Bayesian last layer neural networks. This yields a sampling-free, single-pass model and loss that effectively improves uncertainty estimation. Our variational Bayesian last layer (VBLL) can be trained and evaluated with only quadratic complexity in last layer width, and is thus (nearly) computationally free to add to standard architectures. We experimentally investigate VBLLs, and show that they improve predictive accuracy, calibration, and out of distribution detection over baselines across both regression and classification. Finally, we investigate combining VBLL layers with variational Bayesian feature learning, yielding a lower variance collapsed variational inference method for Bayesian neural networks.

Real-world single image denoising is crucial and practical in computer vision. Bayesian inversions combined with score priors now have proven effective for single image denoising but are limited to white Gaussian noise. Moreover, applying existing score-based methods for real-world denoising requires not only the explicit train of score priors on the target domain but also the careful design of sampling procedures for posterior inference, which is complicated and impractical. To address these limitations, we propose a score priors-guided deep variational inference, namely ScoreDVI, for practical real-world denoising. By considering the deep variational image posterior with a Gaussian form, score priors are extracted based on easily accessible minimum MSE Non-i.i.d Gaussian denoisers and variational samples, which in turn facilitate optimizing the variational image posterior. Such a procedure adaptively applies cheap score priors to denoising. Additionally, we exploit a Non-i.i.d Gaussian mixture model and variational noise posterior to model the real-world noise. This scheme also enables the pixel-wise fusion of multiple image priors and variational image posteriors. Besides, we develop a noise-aware prior assignment strategy that dynamically adjusts the weight of image priors in the optimization. Our method outperforms other single image-based real-world denoising methods and achieves comparable performance to dataset-based unsupervised methods.

Twelve-lead electrocardiograms (ECGs) are the clinical gold standard for cardiac diagnosis, providing comprehensive spatial coverage of the heart necessary to detect conditions such as myocardial infarction (MI). However, their lack of portability limits continuous and large-scale use. Three-lead ECG systems are widely used in wearable devices due to their simplicity and mobility, but they often fail to capture pathologies in unmeasured regions. To address this, we propose WearECG, a Variational Autoencoder (VAE) method that reconstructs twelve-lead ECGs from three leads: II, V1, and V5. Our model includes architectural improvements to better capture temporal and spatial dependencies in ECG signals. We evaluate generation quality using MSE, MAE, and Frechet Inception Distance (FID), and assess clinical validity via a Turing test with expert cardiologists. To further validate diagnostic utility, we fine-tune ECGFounder, a large-scale pretrained ECG model, on a multi-label classification task involving over 40 cardiac conditions, including six different myocardial infarction locations, using both real and generated signals. Experiments on the MIMIC dataset show that our method produces physiologically realistic and diagnostically informative signals, with robust performance in downstream tasks. This work demonstrates the potential of generative modeling for ECG reconstruction and its implications for scalable, low-cost cardiac screening.

In recent years, particle-based variational inference (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popularity as scalable methods for Bayesian inference. Unfortunately, the properties of such methods invariably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate. In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free. We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demonstrating comparable performance to other ParVI algorithms with no need to tune a learning rate.

In meta reinforcement learning (meta RL), an agent seeks a Bayes-optimal policy -- the optimal policy when facing an unknown task that is sampled from some known task distribution. Previous approaches tackled this problem by inferring a belief over task parameters, using variational inference methods. Motivated by recent successes of contrastive learning approaches in RL, such as contrastive predictive coding (CPC), we investigate whether contrastive methods can be used for learning Bayes-optimal behavior. We begin by proving that representations learned by CPC are indeed sufficient for Bayes optimality. Based on this observation, we propose a simple meta RL algorithm that uses CPC in lieu of variational belief inference. Our method, ContraBAR, achieves comparable performance to state-of-the-art in domains with state-based observation and circumvents the computational toll of future observation reconstruction, enabling learning in domains with image-based observations. It can also be combined with image augmentations for domain randomization and used seamlessly in both online and offline meta RL settings.

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains challenging: the high complexity of tree space poses a significant obstacle for the current combinatorial and probabilistic techniques. In this paper, we adopt the framework of generative flow networks (GFlowNets) to tackle two core problems in phylogenetics: parsimony-based and Bayesian phylogenetic inference. Because GFlowNets are well-suited for sampling complex combinatorial structures, they are a natural choice for exploring and sampling from the multimodal posterior distribution over tree topologies and evolutionary distances. We demonstrate that our amortized posterior sampler, PhyloGFN, produces diverse and high-quality evolutionary hypotheses on real benchmark datasets. PhyloGFN is competitive with prior works in marginal likelihood estimation and achieves a closer fit to the target distribution than state-of-the-art variational inference methods. Our code is available at https://github.com/zmy1116/phylogfn.

Several recent end-to-end text-to-speech (TTS) models enabling single-stage training and parallel sampling have been proposed, but their sample quality does not match that of two-stage TTS systems. In this work, we present a parallel end-to-end TTS method that generates more natural sounding audio than current two-stage models. Our method adopts variational inference augmented with normalizing flows and an adversarial training process, which improves the expressive power of generative modeling. We also propose a stochastic duration predictor to synthesize speech with diverse rhythms from input text. With the uncertainty modeling over latent variables and the stochastic duration predictor, our method expresses the natural one-to-many relationship in which a text input can be spoken in multiple ways with different pitches and rhythms. A subjective human evaluation (mean opinion score, or MOS) on the LJ Speech, a single speaker dataset, shows that our method outperforms the best publicly available TTS systems and achieves a MOS comparable to ground truth.

We present latentSplat, a method to predict semantic Gaussians in a 3D latent space that can be splatted and decoded by a light-weight generative 2D architecture. Existing methods for generalizable 3D reconstruction either do not scale to large scenes and resolutions, or are limited to interpolation of close input views. latentSplat combines the strengths of regression-based and generative approaches while being trained purely on readily available real video data. The core of our method are variational 3D Gaussians, a representation that efficiently encodes varying uncertainty within a latent space consisting of 3D feature Gaussians. From these Gaussians, specific instances can be sampled and rendered via efficient splatting and a fast, generative decoder. We show that latentSplat outperforms previous works in reconstruction quality and generalization, while being fast and scalable to high-resolution data.

In this paper, a novel self-supervised learning (SSL) method is proposed, which learns not only representations but also representations uncertainties by considering SSL in terms of variational inference. SSL is a method of learning representation without labels by maximizing the similarity between image representations of different augmented views of the same image. Variational autoencoder (VAE) is an unsupervised representation learning method that trains a probabilistic generative model with variational inference. VAE and SSL can learn representations without labels, but the relationship between VAE and SSL has not been revealed. In this paper, the theoretical relationship between SSL and variational inference is clarified. In addition, variational inference SimSiam (VI-SimSiam) is proposed, which can predict the representation uncertainty by interpreting SimSiam with variational inference and defining the latent space distribution. The experiment qualitatively showed that VISimSiam could learn uncertainty by comparing input images and predicted uncertainties. We also revealed a relationship between estimated uncertainty and classification accuracy.

Diffusion probabilistic models have shown significant progress in video generation; however, their computational efficiency is limited by the large number of sampling steps required. Reducing sampling steps often compromises video quality or generation diversity. In this work, we introduce a distillation method that combines variational score distillation and consistency distillation to achieve few-step video generation, maintaining both high quality and diversity. We also propose a latent reward model fine-tuning approach to further enhance video generation performance according to any specified reward metric. This approach reduces memory usage and does not require the reward to be differentiable. Our method demonstrates state-of-the-art performance in few-step generation for 10-second videos (128 frames at 12 FPS). The distilled student model achieves a score of 82.57 on VBench, surpassing the teacher model as well as baseline models Gen-3, T2V-Turbo, and Kling. One-step distillation accelerates the teacher model's diffusion sampling by up to 278.6 times, enabling near real-time generation. Human evaluations further validate the superior performance of our 4-step student models compared to teacher model using 50-step DDIM sampling.

The idea of video super resolution is to use different view points of a single scene to enhance the overall resolution and quality. Classical energy minimization approaches first establish a correspondence of the current frame to all its neighbors in some radius and then use this temporal information for enhancement. In this paper, we propose the first variational super resolution approach that computes several super resolved frames in one batch optimization procedure by incorporating motion information between the high-resolution image frames themselves. As a consequence, the number of motion estimation problems grows linearly in the number of frames, opposed to a quadratic growth of classical methods and temporal consistency is enforced naturally. We use infimal convolution regularization as well as an automatic parameter balancing scheme to automatically determine the reliability of the motion information and reweight the regularization locally. We demonstrate that our approach yields state-of-the-art results and even is competitive with machine learning approaches.

Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.

While diffusion distillation has enabled one-step generation through methods like Variational Score Distillation, adapting distilled models to emerging new controls -- such as novel structural constraints or latest user preferences -- remains challenging. Conventional approaches typically requires modifying the base diffusion model and redistilling it -- a process that is both computationally intensive and time-consuming. To address these challenges, we introduce Joint Distribution Matching (JDM), a novel approach that minimizes the reverse KL divergence between image-condition joint distributions. By deriving a tractable upper bound, JDM decouples fidelity learning from condition learning. This asymmetric distillation scheme enables our one-step student to handle controls unknown to the teacher model and facilitates improved classifier-free guidance (CFG) usage and seamless integration of human feedback learning (HFL). Experimental results demonstrate that JDM surpasses baseline methods such as multi-step ControlNet by mere one-step in most cases, while achieving state-of-the-art performance in one-step text-to-image synthesis through improved usage of CFG or HFL integration.

Ensuring the quality and integrity of medical images is crucial for maintaining diagnostic accuracy in deep learning-based Computer-Aided Diagnosis and Computer-Aided Detection (CAD) systems. Covariate shifts are subtle variations in the data distribution caused by different imaging devices or settings and can severely degrade model performance, similar to the effects of adversarial attacks. Therefore, it is vital to have a lightweight and fast method to assess the quality of these images prior to using CAD models. AdverX-Ray addresses this need by serving as an image-quality assessment layer, designed to detect covariate shifts effectively. This Adversarial Variational Autoencoder prioritizes the discriminator's role, using the suboptimal outputs of the generator as negative samples to fine-tune the discriminator's ability to identify high-frequency artifacts. Images generated by adversarial networks often exhibit severe high-frequency artifacts, guiding the discriminator to focus excessively on these components. This makes the discriminator ideal for this approach. Trained on patches from X-ray images of specific machine models, AdverX-Ray can evaluate whether a scan matches the training distribution, or if a scan from the same machine is captured under different settings. Extensive comparisons with various OOD detection methods show that AdverX-Ray significantly outperforms existing techniques, achieving a 96.2% average AUROC using only 64 random patches from an X-ray. Its lightweight and fast architecture makes it suitable for real-time applications, enhancing the reliability of medical imaging systems. The code and pretrained models are publicly available.

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

Sampling from diffusion models involves a slow iterative process that hinders their practical deployment, especially for interactive applications. To accelerate generation speed, recent approaches distill a multi-step diffusion model into a single-step student generator via variational score distillation, which matches the distribution of samples generated by the student to the teacher's distribution. However, these approaches use the reverse Kullback-Leibler (KL) divergence for distribution matching which is known to be mode seeking. In this paper, we generalize the distribution matching approach using a novel f-divergence minimization framework, termed f-distill, that covers different divergences with different trade-offs in terms of mode coverage and training variance. We derive the gradient of the f-divergence between the teacher and student distributions and show that it is expressed as the product of their score differences and a weighting function determined by their density ratio. This weighting function naturally emphasizes samples with higher density in the teacher distribution, when using a less mode-seeking divergence. We observe that the popular variational score distillation approach using the reverse-KL divergence is a special case within our framework. Empirically, we demonstrate that alternative f-divergences, such as forward-KL and Jensen-Shannon divergences, outperform the current best variational score distillation methods across image generation tasks. In particular, when using Jensen-Shannon divergence, f-distill achieves current state-of-the-art one-step generation performance on ImageNet64 and zero-shot text-to-image generation on MS-COCO. Project page: https://research.nvidia.com/labs/genair/f-distill

Variational inequalities in general and saddle point problems in particular are increasingly relevant in machine learning applications, including adversarial learning, GANs, transport and robust optimization. With increasing data and problem sizes necessary to train high performing models across various applications, we need to rely on parallel and distributed computing. However, in distributed training, communication among the compute nodes is a key bottleneck during training, and this problem is exacerbated for high dimensional and over-parameterized models. Due to these considerations, it is important to equip existing methods with strategies that would allow to reduce the volume of transmitted information during training while obtaining a model of comparable quality. In this paper, we present the first theoretically grounded distributed methods for solving variational inequalities and saddle point problems using compressed communication: MASHA1 and MASHA2. Our theory and methods allow for the use of both unbiased (such as Randk; MASHA1) and contractive (such as Topk; MASHA2) compressors. New algorithms support bidirectional compressions, and also can be modified for stochastic setting with batches and for federated learning with partial participation of clients. We empirically validated our conclusions using two experimental setups: a standard bilinear min-max problem, and large-scale distributed adversarial training of transformers.

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai.

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.

Recent methods for knowledge grounded dialogs generate responses by incorporating information from an external textual document. These methods do not require the exact document to be known during training and rely on the use of a retrieval system to fetch relevant documents from a large index. The documents used to generate the responses are modeled as latent variables whose prior probabilities need to be estimated. Models such as RAG and REALM, marginalize the document probabilities over the documents retrieved from the index to define the log likelihood loss function which is optimized end-to-end. In this paper, we develop a variational approach to the above technique wherein, we instead maximize the Evidence Lower bound (ELBO). Using a collection of three publicly available open-conversation datasets, we demonstrate how the posterior distribution, that has information from the ground-truth response, allows for a better approximation of the objective function during training. To overcome the challenges associated with sampling over a large knowledge collection, we develop an efficient approach to approximate the ELBO. To the best of our knowledge we are the first to apply variational training for open-scale unsupervised knowledge grounded dialog systems.

We develop a deep variational free energy framework to compute the equation of state of hydrogen in the warm dense matter region. This method parameterizes the variational density matrix of hydrogen nuclei and electrons at finite temperature using three deep generative models: a normalizing flow model that represents the Boltzmann distribution of the classical nuclei, an autoregressive transformer that models the distribution of electrons in excited states, and a permutational equivariant flow model that constructs backflow coordinates for electrons in Hartree-Fock orbitals. By jointly optimizing the three neural networks to minimize the variational free energy, we obtain the equation of state and related thermodynamic properties of dense hydrogen. We compare our results with other theoretical and experimental results on the deuterium Hugoniot curve, aiming to resolve existing discrepancies. The calculated results provide a valuable benchmark for deuterium in the warm dense matter region.

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models. Our code is available at https://github.com/sail-sg/variational-reasoning.

This paper considers a joint scattering environment sensing and data recovery problem in an uplink integrated sensing and communication (ISAC) system. To facilitate joint scatterers localization and multi-user (MU) channel estimation, we introduce a three-dimensional (3D) location-domain sparse channel model to capture the joint sparsity of the MU channel (i.e., different user channels share partially overlapped scatterers). Then the joint problem is formulated as a bilinear structured sparse recovery problem with a dynamic position grid and imperfect parameters (such as time offset and user position errors). We propose an expectation maximization based turbo bilinear subspace variational Bayesian inference (EM-Turbo-BiSVBI) algorithm to solve the problem effectively, where the E-step performs Bayesian estimation of the the location-domain sparse MU channel by exploiting the joint sparsity, and the M-step refines the dynamic position grid and learns the imperfect factors via gradient update. Two methods are introduced to greatly reduce the complexity with almost no sacrifice on the performance and convergence speed: 1) a subspace constrained bilinear variational Bayesian inference (VBI) method is proposed to avoid any high-dimensional matrix inverse; 2) the multiple signal classification (MUSIC) and subspace constrained VBI methods are combined to obtain a coarse estimation result to reduce the search range. Simulations verify the advantages of the proposed scheme over baseline schemes.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

Magnetic Resonance Imaging can produce detailed images of the anatomy and physiology of the human body that can assist doctors in diagnosing and treating pathologies such as tumours. However, MRI suffers from very long acquisition times that make it susceptible to patient motion artifacts and limit its potential to deliver dynamic treatments. Conventional approaches such as Parallel Imaging and Compressed Sensing allow for an increase in MRI acquisition speed by reconstructing MR images from sub-sampled MRI data acquired using multiple receiver coils. Recent advancements in Deep Learning combined with Parallel Imaging and Compressed Sensing techniques have the potential to produce high-fidelity reconstructions from highly accelerated MRI data. In this work we present a novel Deep Learning-based Inverse Problem solver applied to the task of Accelerated MRI Reconstruction, called the Recurrent Variational Network (RecurrentVarNet), by exploiting the properties of Convolutional Recurrent Neural Networks and unrolled algorithms for solving Inverse Problems. The RecurrentVarNet consists of multiple recurrent blocks, each responsible for one iteration of the unrolled variational optimization scheme for solving the inverse problem of multi-coil Accelerated MRI Reconstruction. Contrary to traditional approaches, the optimization steps are performed in the observation domain (k-space) instead of the image domain. Each block of the RecurrentVarNet refines the observed k-space and comprises a data consistency term and a recurrent unit which takes as input a learned hidden state and the prediction of the previous block. Our proposed method achieves new state of the art qualitative and quantitative reconstruction results on 5-fold and 10-fold accelerated data from a public multi-coil brain dataset, outperforming previous conventional and deep learning-based approaches.

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

Multi-view graph clustering (MGC) methods are increasingly being studied due to the explosion of multi-view data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose Variational Graph Generator for Multi-View Graph Clustering (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then a simple yet effective graph encoder in conjunction with the multi-view clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck principle.Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs. The source code is publicly available at https://github.com/cjpcool/VGMGC.

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolutional Hierarchical Deep Neural Network (C-HiDeNN) as the approximation basis. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order p, patch size s) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 10^{10} spatial degrees of freedom (DoFs), our 3-level ML-VMS C-HiDeNN-TD achieves an approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM.

Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to numerically implement the proximal step. The most challenging step, in this setup, is to evaluate functions involving density explicitly, such as entropy, in terms of samples. This paper builds on the recent works with a slight but crucial difference: we propose to utilize a variational formulation of the objective function formulated as maximization over a parametric class of functions. Theoretically, the proposed variational formulation allows the construction of gradient flows directly for empirical distributions with a well-defined and meaningful objective function. Computationally, this approach replaces the computationally expensive step in existing methods, to handle objective functions involving density, with inner loop updates that only require a small batch of samples and scale well with the dimension. The performance and scalability of the proposed method are illustrated with the aid of several numerical experiments involving high-dimensional synthetic and real datasets.

Accumulated clinical studies show that microbes living in humans interact closely with human hosts, and get involved in modulating drug efficacy and drug toxicity. Microbes have become novel targets for the development of antibacterial agents. Therefore, screening of microbe-drug associations can benefit greatly drug research and development. With the increase of microbial genomic and pharmacological datasets, we are greatly motivated to develop an effective computational method to identify new microbe-drug associations. In this paper, we proposed a novel method, Graph2MDA, to predict microbe-drug associations by using variational graph autoencoder (VGAE). We constructed multi-modal attributed graphs based on multiple features of microbes and drugs, such as molecular structures, microbe genetic sequences, and function annotations. Taking as input the multi-modal attribute graphs, VGAE was trained to learn the informative and interpretable latent representations of each node and the whole graph, and then a deep neural network classifier was used to predict microbe-drug associations. The hyperparameter analysis and model ablation studies showed the sensitivity and robustness of our model. We evaluated our method on three independent datasets and the experimental results showed that our proposed method outperformed six existing state-of-the-art methods. We also explored the meaningness of the learned latent representations of drugs and found that the drugs show obvious clustering patterns that are significantly consistent with drug ATC classification. Moreover, we conducted case studies on two microbes and two drugs and found 75\%-95\% predicted associations have been reported in PubMed literature. Our extensive performance evaluations validated the effectiveness of our proposed method.\

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation that lead to degradation in the performance of the underlying model. Major concerns with existing defense mechanisms include non-generalizability across different attacks, models and large inference time. In this paper, we propose a generalized defense mechanism capitalizing on the expressive power of regularized latent space based generative models. We design an adversarial filter, devoid of access to classifier and adversaries, which makes it usable in tandem with any classifier. The basic idea is to learn a Lipschitz constrained mapping from the data manifold, incorporating adversarial perturbations, to a quantized latent space and re-map it to the true data manifold. Specifically, we simultaneously auto-encode the data manifold and its perturbations implicitly through the perturbations of the regularized and quantized generative latent space, realized using variational inference. We demonstrate the efficacy of the proposed formulation in providing resilience against multiple attack types (black and white box) and methods, while being almost real-time. Our experiments show that the proposed method surpasses the state-of-the-art techniques in several cases.

Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

In recent years, there has been a growing emphasis on compressing large pre-trained transformer models for resource-constrained devices. However, traditional pruning methods often leave the embedding layer untouched, leading to model over-parameterization. Additionally, they require extensive compression time with large datasets to maintain performance in pruned models. To address these challenges, we propose VTrans, an iterative pruning framework guided by the Variational Information Bottleneck (VIB) principle. Our method compresses all structural components, including embeddings, attention heads, and layers using VIB-trained masks. This approach retains only essential weights in each layer, ensuring compliance with specified model size or computational constraints. Notably, our method achieves upto 70% more compression than prior state-of-the-art approaches, both task-agnostic and task-specific. We further propose faster variants of our method: Fast-VTrans utilizing only 3% of the data and Faster-VTrans, a time efficient alternative that involves exclusive finetuning of VIB masks, accelerating compression by upto 25 times with minimal performance loss compared to previous methods. Extensive experiments on BERT, ROBERTa, and GPT-2 models substantiate the efficacy of our method. Moreover, our method demonstrates scalability in compressing large models such as LLaMA-2-7B, achieving superior performance compared to previous pruning methods. Additionally, we use attention-based probing to qualitatively assess model redundancy and interpret the efficiency of our approach. Notably, our method considers heads with high attention to special and current tokens in un-pruned model as foremost candidates for pruning while retained heads are observed to attend more to task-critical keywords.

The prior drift is crucial in Continual Test-Time Adaptation (CTTA) methods that only use unlabeled test data, as it can cause significant error propagation. In this paper, we introduce VCoTTA, a variational Bayesian approach to measure uncertainties in CTTA. At the source stage, we transform a pre-trained deterministic model into a Bayesian Neural Network (BNN) via a variational warm-up strategy, injecting uncertainties into the model. During the testing time, we employ a mean-teacher update strategy using variational inference for the student model and exponential moving average for the teacher model. Our novel approach updates the student model by combining priors from both the source and teacher models. The evidence lower bound is formulated as the cross-entropy between the student and teacher models, along with the Kullback-Leibler (KL) divergence of the prior mixture. Experimental results on three datasets demonstrate the method's effectiveness in mitigating prior drift within the CTTA framework.

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended beta-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

Variational autoencoders (VAEs) are one of the powerful unsupervised learning frameworks in NLP for latent representation learning and latent-directed generation. The classic optimization goal of VAEs is to maximize the Evidence Lower Bound (ELBo), which consists of a conditional likelihood for generation and a negative Kullback-Leibler (KL) divergence for regularization. In practice, optimizing ELBo often leads the posterior distribution of all samples converge to the same degenerated local optimum, namely posterior collapse or KL vanishing. There are effective ways proposed to prevent posterior collapse in VAEs, but we observe that they in essence make trade-offs between posterior collapse and hole problem, i.e., mismatch between the aggregated posterior distribution and the prior distribution. To this end, we introduce new training objectives to tackle both two problems through a novel regularization based on the probabilistic density gap between the aggregated posterior distribution and the prior distribution. Through experiments on language modeling, latent space visualization and interpolation, we show that our proposed method can solve both problems effectively and thus outperforms the existing methods in latent-directed generation. To the best of our knowledge, we are the first to jointly solve the hole problem and the posterior collapse.

Visual counterfactual explanation (CF) methods modify image concepts, e.g, shape, to change a prediction to a predefined outcome while closely resembling the original query image. Unlike self-explainable models (SEMs) and heatmap techniques, they grant users the ability to examine hypothetical "what-if" scenarios. Previous CF methods either entail post-hoc training, limiting the balance between transparency and CF quality, or demand optimization during inference. To bridge the gap between transparent SEMs and CF methods, we introduce the GdVAE, a self-explainable model based on a conditional variational autoencoder (CVAE), featuring a Gaussian discriminant analysis (GDA) classifier and integrated CF explanations. Full transparency is achieved through a generative classifier that leverages class-specific prototypes for the downstream task and a closed-form solution for CFs in the latent space. The consistency of CFs is improved by regularizing the latent space with the explainer function. Extensive comparisons with existing approaches affirm the effectiveness of our method in producing high-quality CF explanations while preserving transparency. Code and models are public.

Objective: fMRI and derived measures such as functional connectivity (FC) have been used to predict brain age, general fluid intelligence, psychiatric disease status, and preclinical neurodegenerative disease. However, it is not always clear that all demographic confounds, such as age, sex, and race, have been removed from fMRI data. Additionally, many fMRI datasets are restricted to authorized researchers, making dissemination of these valuable data sources challenging. Methods: We create a variational autoencoder (VAE)-based model, DemoVAE, to decorrelate fMRI features from demographics and generate high-quality synthetic fMRI data based on user-supplied demographics. We train and validate our model using two large, widely used datasets, the Philadelphia Neurodevelopmental Cohort (PNC) and Bipolar and Schizophrenia Network for Intermediate Phenotypes (BSNIP). Results: We find that DemoVAE recapitulates group differences in fMRI data while capturing the full breadth of individual variations. Significantly, we also find that most clinical and computerized battery fields that are correlated with fMRI data are not correlated with DemoVAE latents. An exception are several fields related to schizophrenia medication and symptom severity. Conclusion: Our model generates fMRI data that captures the full distribution of FC better than traditional VAE or GAN models. We also find that most prediction using fMRI data is dependent on correlation with, and prediction of, demographics. Significance: Our DemoVAE model allows for generation of high quality synthetic data conditioned on subject demographics as well as the removal of the confounding effects of demographics. We identify that FC-based prediction tasks are highly influenced by demographic confounds.

Lung cancer is responsible for 21% of cancer deaths in the UK and five-year survival rates are heavily influenced by the stage the cancer was identified at. Recent studies have demonstrated the capability of AI methods for accurate and early diagnosis of lung cancer from routine scans. However, this evidence has not translated into clinical practice with one barrier being a lack of interpretable models. This study investigates the application Variational Autoencoders (VAEs), a type of generative AI model, to lung cancer lesions. Proposed models were trained on lesions extracted from 3D CT scans in the LIDC-IDRI public dataset. Latent vector representations of 2D slices produced by the VAEs were explored through clustering to justify their quality and used in an MLP classifier model for lung cancer diagnosis, the best model achieved state-of-the-art metrics of AUC 0.98 and 93.1% accuracy. Cluster analysis shows the VAE latent space separates the dataset of malignant and benign lesions based on meaningful feature components including tumour size, shape, patient and malignancy class. We also include a comparative analysis of the standard Gaussian VAE (GVAE) and the more recent Dirichlet VAE (DirVAE), which replaces the prior with a Dirichlet distribution to encourage a more explainable latent space with disentangled feature representation. Finally, we demonstrate the potential for latent space traversals corresponding to clinically meaningful feature changes.

Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks, interpretability, etc. We consider the problem of unsupervised learning of disentangled representations from large pool of unlabeled observations, and propose a variational inference based approach to infer disentangled latent factors. We introduce a regularizer on the expectation of the approximate posterior over observed data that encourages the disentanglement. We also propose a new disentanglement metric which is better aligned with the qualitative disentanglement observed in the decoder's output. We empirically observe significant improvement over existing methods in terms of both disentanglement and data likelihood (reconstruction quality).

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

In this paper, we propose to regularize ill-posed inverse problems using a deep hierarchical variational autoencoder (HVAE) as an image prior. The proposed method synthesizes the advantages of i) denoiser-based Plug \& Play approaches and ii) generative model based approaches to inverse problems. First, we exploit VAE properties to design an efficient algorithm that benefits from convergence guarantees of Plug-and-Play (PnP) methods. Second, our approach is not restricted to specialized datasets and the proposed PnP-HVAE model is able to solve image restoration problems on natural images of any size. Our experiments show that the proposed PnP-HVAE method is competitive with both SOTA denoiser-based PnP approaches, and other SOTA restoration methods based on generative models.

Contrastive learning has been successfully used for retrieval of semantically aligned sentences, but it often requires large batch sizes or careful engineering to work well. In this paper, we instead propose a generative model for learning multilingual text embeddings which can be used to retrieve or score sentence pairs. Our model operates on parallel data in N languages and, through an approximation we introduce, efficiently encourages source separation in this multilingual setting, separating semantic information that is shared between translations from stylistic or language-specific variation. We show careful large-scale comparisons between contrastive and generation-based approaches for learning multilingual text embeddings, a comparison that has not been done to the best of our knowledge despite the popularity of these approaches. We evaluate this method on a suite of tasks including semantic similarity, bitext mining, and cross-lingual question retrieval -- the last of which we introduce in this paper. Overall, our Variational Multilingual Source-Separation Transformer (VMSST) model outperforms both a strong contrastive and generative baseline on these tasks.

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking into consideration those geometrical aspects can lead to better interpolations and an improved generation procedure. This new proposed sampling method consists in sampling from the uniform distribution deriving intrinsically from the learned Riemannian latent space and we show that using this scheme can make a vanilla VAE competitive and even better than more advanced versions on several benchmark datasets. Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.

Given the ubiquity of deep neural networks, it is important that these models do not reveal information about sensitive data that they have been trained on. In model inversion attacks, a malicious user attempts to recover the private dataset used to train a supervised neural network. A successful model inversion attack should generate realistic and diverse samples that accurately describe each of the classes in the private dataset. In this work, we provide a probabilistic interpretation of model inversion attacks, and formulate a variational objective that accounts for both diversity and accuracy. In order to optimize this variational objective, we choose a variational family defined in the code space of a deep generative model, trained on a public auxiliary dataset that shares some structural similarity with the target dataset. Empirically, our method substantially improves performance in terms of target attack accuracy, sample realism, and diversity on datasets of faces and chest X-ray images.

We present a novel method for constructing Variational Autoencoder (VAE). Instead of using pixel-by-pixel loss, we enforce deep feature consistency between the input and the output of a VAE, which ensures the VAE's output to preserve the spatial correlation characteristics of the input, thus leading the output to have a more natural visual appearance and better perceptual quality. Based on recent deep learning works such as style transfer, we employ a pre-trained deep convolutional neural network (CNN) and use its hidden features to define a feature perceptual loss for VAE training. Evaluated on the CelebA face dataset, we show that our model produces better results than other methods in the literature. We also show that our method can produce latent vectors that can capture the semantic information of face expressions and can be used to achieve state-of-the-art performance in facial attribute prediction.

Advances in latent diffusion models (LDMs) have revolutionized high-resolution image generation, but the design space of the autoencoder that is central to these systems remains underexplored. In this paper, we introduce LiteVAE, a family of autoencoders for LDMs that leverage the 2D discrete wavelet transform to enhance scalability and computational efficiency over standard variational autoencoders (VAEs) with no sacrifice in output quality. We also investigate the training methodologies and the decoder architecture of LiteVAE and propose several enhancements that improve the training dynamics and reconstruction quality. Our base LiteVAE model matches the quality of the established VAEs in current LDMs with a six-fold reduction in encoder parameters, leading to faster training and lower GPU memory requirements, while our larger model outperforms VAEs of comparable complexity across all evaluated metrics (rFID, LPIPS, PSNR, and SSIM).

Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does not marginalize over latent alignments in a probabilistic sense. This property makes it difficult to compare attention to other alignment approaches, to compose it with probabilistic models, and to perform posterior inference conditioned on observed data. A related latent approach, hard attention, fixes these issues, but is generally harder to train and less accurate. This work considers variational attention networks, alternatives to soft and hard attention for learning latent variable alignment models, with tighter approximation bounds based on amortized variational inference. We further propose methods for reducing the variance of gradients to make these approaches computationally feasible. Experiments show that for machine translation and visual question answering, inefficient exact latent variable models outperform standard neural attention, but these gains go away when using hard attention based training. On the other hand, variational attention retains most of the performance gain but with training speed comparable to neural attention.

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep learning systems). In this setting, the optimal O(1/t) convergence rate for solving smooth monotone variational inequalities is achieved by the Extra-Gradient (EG) algorithm and its variants. Aiming to alleviate the cost of an extra gradient step per iteration (which can become quite substantial in deep learning applications), several algorithms have been proposed as surrogates to Extra-Gradient with a single oracle call per iteration. In this paper, we develop a synthetic view of such algorithms, and we complement the existing literature by showing that they retain a O(1/t) ergodic convergence rate in smooth, deterministic problems. Subsequently, beyond the monotone deterministic case, we also show that the last iterate of single-call, stochastic extra-gradient methods still enjoys a O(1/t) local convergence rate to solutions of non-monotone variational inequalities that satisfy a second-order sufficient condition.

In disentangled representation learning, the goal is to achieve a compact representation that consists of all interpretable generative factors in the observational data. Learning disentangled representations for graphs becomes increasingly important as graph data rapidly grows. Existing approaches often rely on Variational Auto-Encoder (VAE) or its causal structure learning-based refinement, which suffer from sub-optimality in VAEs due to the independence factor assumption and unavailability of concept labels, respectively. In this paper, we propose an unsupervised solution, dubbed concept-free causal disentanglement, built on a theoretically provable tight upper bound approximating the optimal factor. This results in an SCM-like causal structure modeling that directly learns concept structures from data. Based on this idea, we propose Concept-free Causal VGAE (CCVGAE) by incorporating a novel causal disentanglement layer into Variational Graph Auto-Encoder. Furthermore, we prove concept consistency under our concept-free causal disentanglement framework, hence employing it to enhance the meta-learning framework, called concept-free causal Meta-Graph (CC-Meta-Graph). We conduct extensive experiments to demonstrate the superiority of the proposed models: CCVGAE and CC-Meta-Graph, reaching up to 29% and 11% absolute improvements over baselines in terms of AUC, respectively.

We present a novel stochastic variational Gaussian process (GP) inference method, based on a posterior over a learnable set of weighted pseudo input-output points (coresets). Instead of a free-form variational family, the proposed coreset-based, variational tempered family for GPs (CVTGP) is defined in terms of the GP prior and the data-likelihood; hence, accommodating the modeling inductive biases. We derive CVTGP's lower bound for the log-marginal likelihood via marginalization of the proposed posterior over latent GP coreset variables, and show it is amenable to stochastic optimization. CVTGP reduces the learnable parameter size to O(M), enjoys numerical stability, and maintains O(M^3) time- and O(M^2) space-complexity, by leveraging a coreset-based tempered posterior that, in turn, provides sparse and explainable representations of the data. Results on simulated and real-world regression problems with Gaussian observation noise validate that CVTGP provides better evidence lower-bound estimates and predictive root mean squared error than alternative stochastic GP inference methods.

In the loss function of Variational Autoencoders there is a well known tension between two components: the reconstruction loss, improving the quality of the resulting images, and the Kullback-Leibler divergence, acting as a regularizer of the latent space. Correctly balancing these two components is a delicate issue, easily resulting in poor generative behaviours. In a recent work, Dai and Wipf obtained a sensible improvement by allowing the network to learn the balancing factor during training, according to a suitable loss function. In this article, we show that learning can be replaced by a simple deterministic computation, helping to understand the underlying mechanism, and resulting in a faster and more accurate behaviour. On typical datasets such as Cifar and Celeba, our technique sensibly outperforms all previous VAE architectures.

We introduce a Three-Dimensional Convolutional Variational Autoencoder (3D-CVAE) for automated anomaly detection in Electron Energy Loss Spectroscopy Spectrum Imaging (EELS-SI) data. Our approach leverages the full three-dimensional structure of EELS-SI data to detect subtle spectral anomalies while preserving both spatial and spectral correlations across the datacube. By employing negative log-likelihood loss and training on bulk spectra, the model learns to reconstruct bulk features characteristic of the defect-free material. In exploring methods for anomaly detection, we evaluated both our 3D-CVAE approach and Principal Component Analysis (PCA), testing their performance using Fe L-edge peak shifts designed to simulate material defects. Our results show that 3D-CVAE achieves superior anomaly detection and maintains consistent performance across various shift magnitudes. The method demonstrates clear bimodal separation between normal and anomalous spectra, enabling reliable classification. Further analysis verifies that lower dimensional representations are robust to anomalies in the data. While performance advantages over PCA diminish with decreasing anomaly concentration, our method maintains high reconstruction quality even in challenging, noise-dominated spectral regions. This approach provides a robust framework for unsupervised automated detection of spectral anomalies in EELS-SI data, particularly valuable for analyzing complex material systems.

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.

The Poisson equation has wide applications in many areas of science and engineering. Although there are some quantum algorithms that can efficiently solve the Poisson equation, they generally require a fault-tolerant quantum computer which is beyond the current technology. In this paper, we propose a Variational Quantum Algorithm (VQA) to solve the Poisson equation, which can be executed on Noise Intermediate-Scale Quantum (NISQ) devices. In detail, we first adopt the finite difference method to transform the Poisson equation into a linear system. Then, according to the special structure of the linear system, we find an explicit tensor product decomposition, with only 2log n+1 items, of its coefficient matrix under a specific set of simple operators, where n is the dimension of the coefficient matrix. This implies that the proposed VQA only needs O(log n) measurements, which dramatically reduce quantum resources. Additionally, we perform quantum Bell measurements to efficiently evaluate the expectation values of simple operators. Numerical experiments demonstrate that our algorithm can effectively solve the Poisson equation.

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine this variational approximation of the posterior with a similar and efficient SIC-restricted Kullback-Leibler-optimal approximation of the prior. We then focus on a particular SIC ordering and nearest-neighbor-based sparsity pattern resulting in highly accurate prior and posterior approximations. For this setting, our variational approximation can be computed via stochastic gradient descent in polylogarithmic time per iteration. We provide numerical comparisons showing that the proposed double-Kullback-Leibler-optimal Gaussian-process approximation (DKLGP) can sometimes be vastly more accurate for stationary kernels than alternative approaches such as inducing-point and mean-field approximations at similar computational complexity.

Reinforcement Learning from Human Feedback (RLHF) is a powerful paradigm for aligning foundation models to human values and preferences. However, current RLHF techniques cannot account for the naturally occurring differences in individual human preferences across a diverse population. When these differences arise, traditional RLHF frameworks simply average over them, leading to inaccurate rewards and poor performance for individual subgroups. To address the need for pluralistic alignment, we develop a class of multimodal RLHF methods. Our proposed techniques are based on a latent variable formulation - inferring a novel user-specific latent and learning reward models and policies conditioned on this latent without additional user-specific data. While conceptually simple, we show that in practice, this reward modeling requires careful algorithmic considerations around model architecture and reward scaling. To empirically validate our proposed technique, we first show that it can provide a way to combat underspecification in simulated control problems, inferring and optimizing user-specific reward functions. Next, we conduct experiments on pluralistic language datasets representing diverse user preferences and demonstrate improved reward function accuracy. We additionally show the benefits of this probabilistic framework in terms of measuring uncertainty, and actively learning user preferences. This work enables learning from diverse populations of users with divergent preferences, an important challenge that naturally occurs in problems from robot learning to foundation model alignment.

Graph representation learning is a fundamental research theme and can be generalized to benefit multiple downstream tasks from the node and link levels to the higher graph level. In practice, it is desirable to develop task-agnostic general graph representation learning methods that are typically trained in an unsupervised manner. Related research reveals that the power of graph representation learning methods depends on whether they can differentiate distinct graph structures as different embeddings and map isomorphic graphs to consistent embeddings (i.e., the isomorphic consistency of graph models). However, for task-agnostic general graph representation learning, existing unsupervised graph models, represented by the variational graph auto-encoders (VGAEs), can only keep the isomorphic consistency within the subgraphs of 1-hop neighborhoods and thus usually manifest inferior performance on the more difficult higher-level tasks. To overcome the limitations of existing unsupervised methods, in this paper, we propose the Isomorphic-Consistent VGAE (IsoC-VGAE) for multi-level task-agnostic graph representation learning. We first devise a decoding scheme to provide a theoretical guarantee of keeping the isomorphic consistency under the settings of unsupervised learning. We then propose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitive realization, which trains the model via reconstructing the GNN node embeddings with multi-hop neighborhood information, so as to maintain the high-order isomorphic consistency within the VGAE framework. We conduct extensive experiments on the representative graph learning tasks at different levels, including node classification, link prediction and graph classification, and the results verify that our proposed model generally outperforms both the state-of-the-art unsupervised methods and representative supervised methods.

Causal inference plays a vital role in diverse domains like epidemiology, healthcare, and economics. De-confounding and counterfactual prediction in observational data has emerged as a prominent concern in causal inference research. While existing models tackle observed confounders, the presence of unobserved confounders remains a significant challenge, distorting causal inference and impacting counterfactual outcome accuracy. To address this, we propose a novel variational learning model of unobserved confounders for counterfactual inference (VLUCI), which generates the posterior distribution of unobserved confounders. VLUCI relaxes the unconfoundedness assumption often overlooked by most causal inference methods. By disentangling observed and unobserved confounders, VLUCI constructs a doubly variational inference model to approximate the distribution of unobserved confounders, which are used for inferring more accurate counterfactual outcomes. Extensive experiments on synthetic and semi-synthetic datasets demonstrate VLUCI's superior performance in inferring unobserved confounders. It is compatible with state-of-the-art counterfactual inference models, significantly improving inference accuracy at both group and individual levels. Additionally, VLUCI provides confidence intervals for counterfactual outcomes, aiding decision-making in risk-sensitive domains. We further clarify the considerations when applying VLUCI to cases where unobserved confounders don't strictly conform to our model assumptions using the public IHDP dataset as an example, highlighting the practical advantages of VLUCI.

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only global structure and discards information about detailed texture. In this paper, we present a simple but principled method to learn such global representations by combining Variational Autoencoder (VAE) with neural autoregressive models such as RNN, MADE and PixelRNN/CNN. Our proposed VAE model allows us to have control over what the global latent code can learn and , by designing the architecture accordingly, we can force the global latent code to discard irrelevant information such as texture in 2D images, and hence the VAE only "autoencodes" data in a lossy fashion. In addition, by leveraging autoregressive models as both prior distribution p(z) and decoding distribution p(x|z), we can greatly improve generative modeling performance of VAEs, achieving new state-of-the-art results on MNIST, OMNIGLOT and Caltech-101 Silhouettes density estimation tasks.

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields an implicit solvent method identical in form to the Molecular Density Functional theory of Borgis et. al., but with an explicit formula for the 'ideal' free energy term. This new expression for the ideal free energy term can be computed from all-atom molecular dynamics of a solvent with only short-range interactions. The key hypothesis required to make the theory valid is that all smooth (and hence long-range) energy functions obey Gaussian statistics. This is essentially a random phase approximation for perturbations from a short-range only, 'reference,' fluid. This single hypothesis is enough to prove that the self-consistent LMF procedure minimizes a novel density functional whose 'ideal' free energy is the molecular system under a specific, reference Hamiltonian, as opposed to the non-interacting gas of conventional density functionals. Implementation of this new functional into existing software should be straightforward and robust.

The variational autoencoder (VAE) is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a crucial design choice, and it has strong ramifications for the model's performance, such as finding the hidden explanatory factors of a dataset using the representations learned by the VAE. However, the size of the latent dimension of the VAE is often treated as a hyperparameter estimated empirically through trial and error. To this end, we propose a statistical formulation to discover the relevant latent factors required for modeling a dataset. In this work, we use a hierarchical prior in the latent space that estimates the variance of the latent axes using the encoded data, which identifies the relevant latent dimensions. For this, we replace the fixed prior in the VAE objective function with a hierarchical prior, keeping the remainder of the formulation unchanged. We call the proposed method the automatic relevancy detection in the variational autoencoder (ARD-VAE). We demonstrate the efficacy of the ARD-VAE on multiple benchmark datasets in finding the relevant latent dimensions and their effect on different evaluation metrics, such as FID score and disentanglement analysis.

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning can be employed to learn such parameters from data. However, neither exact function values nor exact gradients with respect to the hyperparameters are attainable, necessitating methods that only rely on inexact evaluation of such quantities. State-of-the-art inexact gradient-based methods a priori select a sequence of the required accuracies and cannot identify an appropriate step size since the Lipschitz constant of the hypergradient is unknown. In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point. Furthermore, the proposed algorithm determines the required accuracy dynamically rather than manually selected before running it. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation on a range of relevant problems in imaging and data science such as total variation and field of experts denoising and multinomial logistic regression. Particularly, the results show that the algorithm is robust to its own hyperparameters such as the initial accuracies and step size.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems. However, the existing methods entail computationally demanding iterative sampling procedures and optimize a separate solution for each measurement, which leads to limited scalability and lack of generalization capability across unseen samples. To address these limitations, we propose a novel approach, Diffusion prior-based Amortized Variational Inference (DAVI) that solves inverse problems with a diffusion prior from an amortized variational inference perspective. Specifically, instead of separate measurement-wise optimization, our amortized inference learns a function that directly maps measurements to the implicit posterior distributions of corresponding clean data, enabling a single-step posterior sampling even for unseen measurements. Extensive experiments on image restoration tasks, e.g., Gaussian deblur, 4times super-resolution, and box inpainting with two benchmark datasets, demonstrate our approach's superior performance over strong baselines. Code is available at https://github.com/mlvlab/DAVI.

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic convergence results are derived under strong assumptions such as the boundedness of the gradient noise variance or of the objective's gradient itself. In this paper, we propose several algorithms with high-probability convergence results under less restrictive assumptions. In particular, we derive new high-probability convergence results under the assumption that the gradient/operator noise has bounded central alpha-th moment for alpha in (1,2] in the following setups: (i) smooth non-convex / Polyak-Lojasiewicz / convex / strongly convex / quasi-strongly convex minimization problems, (ii) Lipschitz / star-cocoercive and monotone / quasi-strongly monotone variational inequalities. These results justify the usage of the considered methods for solving problems that do not fit standard functional classes studied in stochastic optimization.

Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been one of the most interesting areas to study, and it is also one of the biggest problems of biochemistry. Each protein folds distinctively, and the difficulty of finding its stable shape rapidly increases with an increase in the number of amino acids in the chain. A moderate protein has about 100 amino acids, and the number of combinations one needs to verify to find the stable structure is enormous. At some point, the number of these combinations will be so vast that classical computers cannot even attempt to solve them. In this paper, we examine how this problem can be solved with the help of quantum computing using two different algorithms, Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), using Qiskit Nature. We compare the results of different quantum hardware and simulators and check how error mitigation affects the performance. Further, we make comparisons with SoTA algorithms and evaluate the reliability of the method.

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim, 2021, Pethick et al., 2022, B\"ohm, 2022] aiming at going beyond monotonicity by considering the weaker negative comonotonicity assumption. In particular, we provide tight complexity analyses for the Proximal Point, Extragradient, and Optimistic Gradient methods in this setup, closing some questions on their working guarantees beyond monotonicity.

In multi-goal Reinforcement Learning, an agent can share experience between related training tasks, resulting in better generalization for new tasks at test time. However, when the goal space has discontinuities and the reward is sparse, a majority of goals are difficult to reach. In this context, a curriculum over goals helps agents learn by adapting training tasks to their current capabilities. In this work we propose Stein Variational Goal Generation (SVGG), which samples goals of intermediate difficulty for the agent, by leveraging a learned predictive model of its goal reaching capabilities. The distribution of goals is modeled with particles that are attracted in areas of appropriate difficulty using Stein Variational Gradient Descent. We show that SVGG outperforms state-of-the-art multi-goal Reinforcement Learning methods in terms of success coverage in hard exploration problems, and demonstrate that it is endowed with a useful recovery property when the environment changes.

Meta-learning algorithms are able to learn a new task using previously learned knowledge, but they often require a large number of meta-training tasks which may not be readily available. To address this issue, we propose a method for few-shot learning with fewer tasks, which we call MetaModulation. The key idea is to use a neural network to increase the density of the meta-training tasks by modulating batch normalization parameters during meta-training. Additionally, we modify parameters at various network levels, rather than just a single layer, to increase task diversity. To account for the uncertainty caused by the limited training tasks, we propose a variational MetaModulation where the modulation parameters are treated as latent variables. We also introduce learning variational feature hierarchies by the variational MetaModulation, which modulates features at all layers and can consider task uncertainty and generate more diverse tasks. The ablation studies illustrate the advantages of utilizing a learnable task modulation at different levels and demonstrate the benefit of incorporating probabilistic variants in few-task meta-learning. Our MetaModulation and its variational variants consistently outperform state-of-the-art alternatives on four few-task meta-learning benchmarks.

Deep learning techniques have dominated the literature on aspect-based sentiment analysis (ABSA), yielding state-of-the-art results. However, these deep models generally suffer from spurious correlation problems between input features and output labels, which creates significant barriers to robustness and generalization capability. In this paper, we propose a novel Contrastive Variational Information Bottleneck framework (called CVIB) to reduce spurious correlations for ABSA. The proposed CVIB framework is composed of an original network and a self-pruned network, and these two networks are optimized simultaneously via contrastive learning. Concretely, we employ the Variational Information Bottleneck (VIB) principle to learn an informative and compressed network (self-pruned network) from the original network, which discards the superfluous patterns or spurious correlations between input features and prediction labels. Then, self-pruning contrastive learning is devised to pull together semantically similar positive pairs and push away dissimilar pairs, where the representations of the anchor learned by the original and self-pruned networks respectively are regarded as a positive pair while the representations of two different sentences within a mini-batch are treated as a negative pair. To verify the effectiveness of our CVIB method, we conduct extensive experiments on five benchmark ABSA datasets and the experimental results show that our approach achieves better performance than the strong competitors in terms of overall prediction performance, robustness, and generalization.

The past several years have witnessed Variational Auto-Encoder's superiority in various text generation tasks. However, due to the sequential nature of the text, auto-regressive decoders tend to ignore latent variables and then reduce to simple language models, known as the KL vanishing problem, which would further deteriorate when VAE is combined with Transformer-based structures. To ameliorate this problem, we propose DELLA, a novel variational Transformer framework. DELLA learns a series of layer-wise latent variables with each inferred from those of lower layers and tightly coupled with the hidden states by low-rank tensor product. In this way, DELLA forces these posterior latent variables to be fused deeply with the whole computation path and hence incorporate more information. We theoretically demonstrate that our method can be regarded as entangling latent variables to avoid posterior information decrease through layers, enabling DELLA to get higher non-zero KL values even without any annealing or thresholding tricks. Experiments on four unconditional and three conditional generation tasks show that DELLA could better alleviate KL vanishing and improve both quality and diversity compared to several strong baselines.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

Multi-speaker text-to-speech (TTS) using a few adaption data is a challenge in practical applications. To address that, we propose a zero-shot multi-speaker TTS, named nnSpeech, that could synthesis a new speaker voice without fine-tuning and using only one adaption utterance. Compared with using a speaker representation module to extract the characteristics of new speakers, our method bases on a speaker-guided conditional variational autoencoder and can generate a variable Z, which contains both speaker characteristics and content information. The latent variable Z distribution is approximated by another variable conditioned on reference mel-spectrogram and phoneme. Experiments on the English corpus, Mandarin corpus, and cross-dataset proves that our model could generate natural and similar speech with only one adaption speech.

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics models into deep generative models. In particular, we introduce an architecture of variational autoencoders (VAEs) in which a part of the latent space is grounded by physics. A key technical challenge is to strike a balance between the incomplete physics and trainable components such as neural networks for ensuring that the physics part is used in a meaningful manner. To this end, we propose a regularized learning method that controls the effect of the trainable components and preserves the semantics of the physics-based latent variables as intended. We not only demonstrate generative performance improvements over a set of synthetic and real-world datasets, but we also show that we learn robust models that can consistently extrapolate beyond the training distribution in a meaningful manner. Moreover, we show that we can control the generative process in an interpretable manner.

Multi-agent coordination is crucial for reliable multi-robot navigation in shared spaces such as automated warehouses. In regions of dense robot traffic, local coordination methods may fail to find a deadlock-free solution. In these scenarios, it is appropriate to let a central unit generate a global schedule that decides the passing order of robots. However, the runtime of such centralized coordination methods increases significantly with the problem scale. In this paper, we propose to leverage Graph Neural Network Variational Autoencoders (GNN-VAE) to solve the multi-agent coordination problem at scale faster than through centralized optimization. We formulate the coordination problem as a graph problem and collect ground truth data using a Mixed-Integer Linear Program (MILP) solver. During training, our learning framework encodes good quality solutions of the graph problem into a latent space. At inference time, solution samples are decoded from the sampled latent variables, and the lowest-cost sample is selected for coordination. Finally, the feasible proposal with the highest performance index is selected for the deployment. By construction, our GNN-VAE framework returns solutions that always respect the constraints of the considered coordination problem. Numerical results show that our approach trained on small-scale problems can achieve high-quality solutions even for large-scale problems with 250 robots, being much faster than other baselines. Project page: https://mengyuest.github.io/gnn-vae-coord

State-of-the-art (SOTA) reinforcement learning (RL) methods enable the vision-language agents to learn from interactions with the environment without human supervision. However, they struggle with learning inefficiencies in tackling real-world complex sequential decision-making tasks, especially with sparse reward signals and long-horizon dependencies. To effectively address the issue, we introduce Variational Subgoal-Conditioned RL (VSC-RL), which reformulates the vision-language sequential decision-making task as a variational goal-conditioned RL problem, allowing us to leverage advanced optimization methods to enhance learning efficiency. Specifically, VSC-RL optimizes the SubGoal Evidence Lower BOund (SGC-ELBO), which consists of (a) maximizing the subgoal-conditioned return via RL and (b) minimizing the subgoal-conditioned difference with the reference policy. We theoretically demonstrate that SGC-ELBO is equivalent to the original optimization objective, ensuring improved learning efficiency without sacrificing performance guarantees. Additionally, for real-world complex decision-making tasks, VSC-RL leverages the vision-language model to autonomously decompose the goal into feasible subgoals, enabling efficient learning. Across various benchmarks, including challenging real-world mobile device control tasks, VSC-RL significantly outperforms the SOTA vision-language agents, achieving superior performance and remarkable improvement in learning efficiency.

We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs excel especially in low-data regimes, where it outperforms existing methods by an order of magnitude in mean squared error for imputation task.

We present Variational Self-Supervised Learning (VSSL), a novel framework that combines variational inference with self-supervised learning to enable efficient, decoder-free representation learning. Unlike traditional VAEs that rely on input reconstruction via a decoder, VSSL symmetrically couples two encoders with Gaussian outputs. A momentum-updated teacher network defines a dynamic, data-dependent prior, while the student encoder produces an approximate posterior from augmented views. The reconstruction term in the ELBO is replaced with a cross-view denoising objective, preserving the analytical tractability of Gaussian KL divergence. We further introduce cosine-based formulations of KL and log-likelihood terms to enhance semantic alignment in high-dimensional latent spaces. Experiments on CIFAR-10, CIFAR-100, and ImageNet-100 show that VSSL achieves competitive or superior performance to leading self-supervised methods, including BYOL and MoCo V3. VSSL offers a scalable, probabilistically grounded approach to learning transferable representations without generative reconstruction, bridging the gap between variational modeling and modern self-supervised techniques.

Many methods have been proposed for removing batch effects and aligning single-cell RNA (scRNA) datasets. However, performance is typically evaluated based on multiple parameters and few datasets, creating challenges in assessing which method is best for aligning data at scale. Here, we introduce the K-Neighbors Intersection (KNI) score, a single score that both penalizes batch effects and measures accuracy at cross-dataset cell-type label prediction alongside carefully curated small (scMARK) and large (scREF) benchmarks comprising 11 and 46 human scRNA studies respectively, where we have standardized author labels. Using the KNI score, we evaluate and optimize approaches for cross-dataset single-cell RNA integration. We introduce Batch Adversarial single-cell Variational Inference (BA-scVI), as a new variant of scVI that uses adversarial training to penalize batch-effects in the encoder and decoder, and show this approach outperforms other methods. In the resulting aligned space, we find that the granularity of cell-type groupings is conserved, supporting the notion that whole-organism cell-type maps can be created by a single model without loss of information.

Existing zero-shot skeleton-based action recognition methods utilize projection networks to learn a shared latent space of skeleton features and semantic embeddings. The inherent imbalance in action recognition datasets, characterized by variable skeleton sequences yet constant class labels, presents significant challenges for alignment. To address the imbalance, we propose SA-DVAE -- Semantic Alignment via Disentangled Variational Autoencoders, a method that first adopts feature disentanglement to separate skeleton features into two independent parts -- one is semantic-related and another is irrelevant -- to better align skeleton and semantic features. We implement this idea via a pair of modality-specific variational autoencoders coupled with a total correction penalty. We conduct experiments on three benchmark datasets: NTU RGB+D, NTU RGB+D 120 and PKU-MMD, and our experimental results show that SA-DAVE produces improved performance over existing methods. The code is available at https://github.com/pha123661/SA-DVAE.

Consistency Training (CT) has recently emerged as a promising alternative to diffusion models, achieving competitive performance in image generation tasks. However, non-distillation consistency training often suffers from high variance and instability, and analyzing and improving its training dynamics is an active area of research. In this work, we propose a novel CT training approach based on the Flow Matching framework. Our main contribution is a trained noise-coupling scheme inspired by the architecture of Variational Autoencoders (VAE). By training a data-dependent noise emission model implemented as an encoder architecture, our method can indirectly learn the geometry of the noise-to-data mapping, which is instead fixed by the choice of the forward process in classical CT. Empirical results across diverse image datasets show significant generative improvements, with our model outperforming baselines and achieving the state-of-the-art (SoTA) non-distillation CT FID on CIFAR-10, and attaining FID on par with SoTA on ImageNet at 64 times 64 resolution in 2-step generation. Our code is available at https://github.com/sony/vct .

Ultra-high-resolution image synthesis holds significant potential, yet remains an underexplored challenge due to the absence of standardized benchmarks and computational constraints. In this paper, we establish Aesthetic-4K, a meticulously curated dataset containing dedicated training and evaluation subsets specifically designed for comprehensive research on ultra-high-resolution image synthesis. This dataset consists of high-quality 4K images accompanied by descriptive captions generated by GPT-4o. Furthermore, we propose Diffusion-4K, an innovative framework for the direct generation of ultra-high-resolution images. Our approach incorporates the Scale Consistent Variational Auto-Encoder (SC-VAE) and Wavelet-based Latent Fine-tuning (WLF), which are designed for efficient visual token compression and the capture of intricate details in ultra-high-resolution images, thereby facilitating direct training with photorealistic 4K data. This method is applicable to various latent diffusion models and demonstrates its efficacy in synthesizing highly detailed 4K images. Additionally, we propose novel metrics, namely the GLCM Score and Compression Ratio, to assess the texture richness and fine details in local patches, in conjunction with holistic measures such as FID, Aesthetics, and CLIPScore, enabling a thorough and multifaceted evaluation of ultra-high-resolution image synthesis. Consequently, Diffusion-4K achieves impressive performance in ultra-high-resolution image synthesis, particularly when powered by state-of-the-art large-scale diffusion models (eg, Flux-12B). The source code is publicly available at https://github.com/zhang0jhon/diffusion-4k.

Despite their ability to generate high-resolution and diverse images from text prompts, text-to-image diffusion models often suffer from slow iterative sampling processes. Model distillation is one of the most effective directions to accelerate these models. However, previous distillation methods fail to retain the generation quality while requiring a significant amount of images for training, either from real data or synthetically generated by the teacher model. In response to this limitation, we present a novel image-free distillation scheme named SwiftBrush. Drawing inspiration from text-to-3D synthesis, in which a 3D neural radiance field that aligns with the input prompt can be obtained from a 2D text-to-image diffusion prior via a specialized loss without the use of any 3D data ground-truth, our approach re-purposes that same loss for distilling a pretrained multi-step text-to-image model to a student network that can generate high-fidelity images with just a single inference step. In spite of its simplicity, our model stands as one of the first one-step text-to-image generators that can produce images of comparable quality to Stable Diffusion without reliance on any training image data. Remarkably, SwiftBrush achieves an FID score of 16.67 and a CLIP score of 0.29 on the COCO-30K benchmark, achieving competitive results or even substantially surpassing existing state-of-the-art distillation techniques.

Vector quantized variational autoencoder (VQ-VAE) is a discrete auto-encoder that compresses images into discrete tokens. It is difficult to train due to discretization. In this paper, we propose a simple yet effective technique, dubbed Gaussian Quant (GQ), that converts a Gaussian VAE with certain constraint into a VQ-VAE without training. GQ generates random Gaussian noise as a codebook and finds the closest noise to the posterior mean. Theoretically, we prove that when the logarithm of the codebook size exceeds the bits-back coding rate of the Gaussian VAE, a small quantization error is guaranteed. Practically, we propose a heuristic to train Gaussian VAE for effective GQ, named target divergence constraint (TDC). Empirically, we show that GQ outperforms previous VQ-VAEs, such as VQGAN, FSQ, LFQ, and BSQ, on both UNet and ViT architectures. Furthermore, TDC also improves upon previous Gaussian VAE discretization methods, such as TokenBridge. The source code is provided in https://github.com/tongdaxu/VQ-VAE-from-Gaussian-VAE.

Autoregressive transformers have revolutionized high-fidelity image generation. One crucial ingredient lies in the tokenizer, which compresses high-resolution image patches into manageable discrete tokens with a scanning or hierarchical order suitable for large language models. Extending these tokenizers to 3D generation, however, presents a significant challenge: unlike image patches that naturally exhibit spatial sequence and multi-scale relationships, 3D data lacks an inherent order, making it difficult to compress into fewer tokens while preserving structural details. To address this, we introduce the Variational Tokenizer (VAT), which transforms unordered 3D data into compact latent tokens with an implicit hierarchy, suited for efficient and high-fidelity coarse-to-fine autoregressive modeling. VAT begins with an in-context transformer, which compress numerous unordered 3D features into a reduced token set with minimal information loss. This latent space is then mapped to a Gaussian distribution for residual quantization, with token counts progressively increasing across scales. In this way, tokens at different scales naturally establish the interconnections by allocating themselves into different subspaces within the same Gaussian distribution, facilitating discrete modeling of token relationships across scales. During the decoding phase, a high-resolution triplane is utilized to convert these compact latent tokens into detailed 3D shapes. Extensive experiments demonstrate that VAT enables scalable and efficient 3D generation, outperforming existing methods in quality, efficiency, and generalization. Remarkably, VAT achieves up to a 250x compression, reducing a 1MB mesh to just 3.9KB with a 96% F-score, and can further compress to 256 int8 tokens, achieving a 2000x reduction while maintaining a 92% F-score.

Vector quantization (VQ) transforms continuous image features into discrete representations, providing compressed, tokenized inputs for generative models. However, VQ-based frameworks suffer from several issues, such as non-smooth latent spaces, weak alignment between representations before and after quantization, and poor coherence between the continuous and discrete domains. These issues lead to unstable codeword learning and underutilized codebooks, ultimately degrading the performance of both reconstruction and downstream generation tasks. To this end, we propose VAEVQ, which comprises three key components: (1) Variational Latent Quantization (VLQ), replacing the AE with a VAE for quantization to leverage its structured and smooth latent space, thereby facilitating more effective codeword activation; (2) Representation Coherence Strategy (RCS), adaptively modulating the alignment strength between pre- and post-quantization features to enhance consistency and prevent overfitting to noise; and (3) Distribution Consistency Regularization (DCR), aligning the entire codebook distribution with the continuous latent distribution to improve utilization. Extensive experiments on two benchmark datasets demonstrate that VAEVQ outperforms state-of-the-art methods.

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem in logistics. Augmented Lagrangian Methods (ALM) for solving CVRP performance depends heavily on well-tuned penalty parameters. In this paper, we propose a hybrid optimization approach that integrates deep reinforcement learning (RL) to automate the selection of penalty parameter values within both classical (RL-C-ALM) and quantum-enhanced (RL-Q-ALM) ALM solvers. Using Soft Actor-Critic, our approach learns penalty values from CVRP instance features and constraint violations. In RL-Q-ALM, subproblems are encoded as QUBOs and solved using Variational Quantum Eigensolvers (VQE). The agent learns across episodes by maximizing solution feasibility and minimizing cost. Experiments show that RL-C-ALM outperforms manually tuned ALM on synthetic and benchmark CVRP instances, achieving better solutions with fewer iterations. Also, RL-Q-ALM matches classical solution quality on small instances but incurs higher runtimes due to quantum overhead. Our results highlight the potential of combining RL with classical and quantum solvers for scalable, adaptive combinatorial optimization.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).

Text-to-Image (T2I) Diffusion Models have achieved remarkable performance in generating high quality images. However, enabling precise control of continuous attributes, especially multiple attributes simultaneously, in a new domain (e.g., numeric values like eye openness or car width) with text-only guidance remains a significant challenge. To address this, we introduce the Attribute (Att) Adapter, a novel plug-and-play module designed to enable fine-grained, multi-attributes control in pretrained diffusion models. Our approach learns a single control adapter from a set of sample images that can be unpaired and contain multiple visual attributes. The Att-Adapter leverages the decoupled cross attention module to naturally harmonize the multiple domain attributes with text conditioning. We further introduce Conditional Variational Autoencoder (CVAE) to the Att-Adapter to mitigate overfitting, matching the diverse nature of the visual world. Evaluations on two public datasets show that Att-Adapter outperforms all LoRA-based baselines in controlling continuous attributes. Additionally, our method enables a broader control range and also improves disentanglement across multiple attributes, surpassing StyleGAN-based techniques. Notably, Att-Adapter is flexible, requiring no paired synthetic data for training, and is easily scalable to multiple attributes within a single model.

Recent 3D content generation pipelines commonly employ Variational Autoencoders (VAEs) to encode shapes into compact latent representations for diffusion-based generation. However, the widely adopted uniform point sampling strategy in Shape VAE training often leads to a significant loss of geometric details, limiting the quality of shape reconstruction and downstream generation tasks. We present Dora-VAE, a novel approach that enhances VAE reconstruction through our proposed sharp edge sampling strategy and a dual cross-attention mechanism. By identifying and prioritizing regions with high geometric complexity during training, our method significantly improves the preservation of fine-grained shape features. Such sampling strategy and the dual attention mechanism enable the VAE to focus on crucial geometric details that are typically missed by uniform sampling approaches. To systematically evaluate VAE reconstruction quality, we additionally propose Dora-bench, a benchmark that quantifies shape complexity through the density of sharp edges, introducing a new metric focused on reconstruction accuracy at these salient geometric features. Extensive experiments on the Dora-bench demonstrate that Dora-VAE achieves comparable reconstruction quality to the state-of-the-art dense XCube-VAE while requiring a latent space at least 8times smaller (1,280 vs. > 10,000 codes).

We introduce a modality-agnostic neural compression algorithm based on a functional view of data and parameterised as an Implicit Neural Representation (INR). Bridging the gap between latent coding and sparsity, we obtain compact latent representations non-linearly mapped to a soft gating mechanism. This allows the specialisation of a shared INR network to each data item through subnetwork selection. After obtaining a dataset of such latent representations, we directly optimise the rate/distortion trade-off in a modality-agnostic space using neural compression. Variational Compression of Implicit Neural Representations (VC-INR) shows improved performance given the same representational capacity pre quantisation while also outperforming previous quantisation schemes used for other INR techniques. Our experiments demonstrate strong results over a large set of diverse modalities using the same algorithm without any modality-specific inductive biases. We show results on images, climate data, 3D shapes and scenes as well as audio and video, introducing VC-INR as the first INR-based method to outperform codecs as well-known and diverse as JPEG 2000, MP3 and AVC/HEVC on their respective modalities.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward chi^2 divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

Positive-unlabeled learning (PU learning) in hyperspectral remote sensing imagery (HSI) is aimed at learning a binary classifier from positive and unlabeled data, which has broad prospects in various earth vision applications. However, when PU learning meets limited labeled HSI, the unlabeled data may dominate the optimization process, which makes the neural networks overfit the unlabeled data. In this paper, a Taylor variational loss is proposed for HSI PU learning, which reduces the weight of the gradient of the unlabeled data by Taylor series expansion to enable the network to find a balance between overfitting and underfitting. In addition, the self-calibrated optimization strategy is designed to stabilize the training process. Experiments on 7 benchmark datasets (21 tasks in total) validate the effectiveness of the proposed method. Code is at: https://github.com/Hengwei-Zhao96/T-HOneCls.

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.