Unity by Diversity: Improved Representation Learning in Multimodal VAEs

Variational Autoencoders for multimodal data hold promise for many tasks in data analysis, such as representation learning, conditional generation, and imputation. Current architectures either share the encoder output, decoder input, or both across modalities to learn a shared representation. Such architectures impose hard constraints on the model. In this work, we show that a better latent representation can be obtained by replacing these hard constraints with a soft constraint. We propose a new mixture-of-experts prior, softly guiding each modality's latent representation towards a shared aggregate posterior. This approach results in a superior latent representation and allows each encoding to preserve information from its uncompressed original features better. In extensive experiments on multiple benchmark datasets and a challenging real-world neuroscience data set, we show improved learned latent representations and imputation of missing data modalities compared to existing methods.

On the Challenges and Opportunities in Generative AI

The field of deep generative modeling has grown rapidly and consistently over the years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models do not sufficiently address several fundamental issues that hinder their widespread adoption across domains. In this work, we aim to identify key unresolved challenges in modern generative AI paradigms that should be tackled to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with valuable insights for exploring fruitful research directions, thereby fostering the development of more robust and accessible generative AI solutions.

Towards Fast Stochastic Sampling in Diffusion Generative Models

Diffusion models suffer from slow sample generation at inference time. Despite recent efforts, improving the sampling efficiency of stochastic samplers for diffusion models remains a promising direction. We propose Splitting Integrators for fast stochastic sampling in pre-trained diffusion models in augmented spaces. Commonly used in molecular dynamics, splitting-based integrators attempt to improve sampling efficiency by cleverly alternating between numerical updates involving the data, auxiliary, or noise variables. However, we show that a naive application of splitting integrators is sub-optimal for fast sampling. Consequently, we propose several principled modifications to naive splitting samplers for improving sampling efficiency and denote the resulting samplers as Reduced Splitting Integrators. In the context of Phase Space Langevin Diffusion (PSLD) [Pandey \& Mandt, 2023] on CIFAR-10, our stochastic sampler achieves an FID score of 2.36 in only 100 network function evaluations (NFE) as compared to 2.63 for the best baselines.

Position Paper: Bayesian Deep Learning in the Age of Large-Scale AI

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

Probabilistic Precipitation Downscaling with Optical Flow-Guided Diffusion

In climate science and meteorology, local precipitation predictions are limited by the immense computational costs induced by the high spatial resolution that simulation methods require. A common workaround is statistical downscaling (aka superresolution), where a low-resolution prediction is super-resolved using statistical approaches. While traditional computer vision tasks mainly focus on human perception or mean squared error, applications in weather and climate require capturing the conditional distribution of high-resolution patterns given low-resolution patterns so that reliable ensemble averages can be taken. Our approach relies on extending recent video diffusion models to precipitation superresolution: an optical flow on the high-resolution output induces temporally coherent predictions, whereas a temporally-conditioned diffusion model generates residuals that capture the correct noise characteristics and high-frequency patterns. We test our approach on X-SHiELD, an established large-scale climate simulation dataset, and compare against two state-of-the-art baselines, focusing on CRPS, MSE, precipitation distributions, as well as an illustrative case -- the complex terrain of California. Our approach sets a new standard for data-driven precipitation downscaling.

Anytime-Valid Confidence Sequences for Consistent Uncertainty Estimation in Early-Exit Neural Networks

Early-exit neural networks (EENNs) facilitate adaptive inference by producing predictions at multiple stages of the forward pass. In safety-critical applications, these predictions are only meaningful when complemented with reliable uncertainty estimates. Yet, due to their sequential structure, an EENN's uncertainty estimates should also be consistent: labels that are deemed improbable at one exit should not reappear within the confidence interval / set of later exits. We show that standard uncertainty quantification techniques, like Bayesian methods or conformal prediction, can lead to inconsistency across exits. We address this problem by applying anytime-valid confidence sequences (AVCSs) to the exits of EENNs. By design, AVCSs maintain consistency across exits. We examine the theoretical and practical challenges of applying AVCSs to EENNs and empirically validate our approach on both regression and classification tasks.

Understanding and Visualizing Droplet Distributions in Simulations of Shallow Clouds

Thorough analysis of local droplet-level interactions is crucial to better understand the microphysical processes in clouds and their effect on the global climate. High-accuracy simulations of relevant droplet size distributions from Large Eddy Simulations (LES) of bin microphysics challenge current analysis techniques due to their high dimensionality involving three spatial dimensions, time, and a continuous range of droplet sizes. Utilizing the compact latent representations from Variational Autoencoders (VAEs), we produce novel and intuitive visualizations for the organization of droplet sizes and their evolution over time beyond what is possible with clustering techniques. This greatly improves interpretation and allows us to examine aerosol-cloud interactions by contrasting simulations with different aerosol concentrations. We find that the evolution of the droplet spectrum is similar across aerosol levels but occurs at different paces. This similarity suggests that precipitation initiation processes are alike despite variations in onset times.

Estimating the Rate-Distortion Function by Wasserstein Gradient Descent

In the theory of lossy compression, the rate-distortion (R-D) function $R(D)$ describes how much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion). Obtaining $R(D)$ for a given data source establishes the fundamental performance limit for all compression algorithms. We propose a new method to estimate $R(D)$ from the perspective of optimal transport. Unlike the classic Blahut--Arimoto algorithm which fixes the support of the reproduction distribution in advance, our Wasserstein gradient descent algorithm learns the support of the optimal reproduction distribution by moving particles. We prove its local convergence and analyze the sample complexity of our R-D estimator based on a connection to entropic optimal transport. Experimentally, we obtain comparable or tighter bounds than state-of-the-art neural network methods on low-rate sources while requiring considerably less tuning and computation effort. We also highlight a connection to maximum-likelihood deconvolution and introduce a new class of sources that can be used as test cases with known solutions to the R-D problem.

Efficient Integrators for Diffusion Generative Models

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at \url{https://github.com/mandt-lab/PSLD}.