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Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn…

Single-cell foundation models learn by reconstructing masked gene expression, implicitly treating technical noise as signal. With dropout rates exceeding 90%, reconstruction objectives encourage models to encode measurement artifacts rather…

Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often…

Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…

Developing deep generative models that flexibly incorporate diverse measures of probability distance is an important area of research. Here we develop an unified mathematical framework of f-divergence generative model, f-GM, that…

Vector Quantized Variational Autoencoders (VQ-VAEs) are fundamental to modern generative modeling, yet they often suffer from training instability and "codebook collapse" due to the inherent coupling of representation learning and discrete…

A variational autoencoder (VAE) is a probabilistic machine learning framework for posterior inference that projects an input set of high-dimensional data to a lower-dimensional, latent space. The latent space learned with a VAE offers…

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…

We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing deep learning approaches either assume access to the driving…

Computer Vision has proven to be a powerful tool for analyzing Spatial Transcriptomics (ST) data. However, current models that predict spatially resolved gene expression from histopathology images suffer from significant limitations due to…

Deep generative models have emerged as influential instruments for data generation and manipulation. Enhancing the controllability of these models by selectively modifying data attributes has been a recent focus. Variational Autoencoders…

Despite recent successes in synthesizing faces and bedrooms, existing generative models struggle to capture more complex image types, potentially due to the oversimplification of their latent space constructions. To tackle this issue,…

We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned…

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…

We introduce Exemplar VAEs, a family of generative models that bridge the gap between parametric and non-parametric, exemplar based generative models. Exemplar VAE is a variant of VAE with a non-parametric prior in the latent space based on…

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…

Variational autoencoders (VAEs) typically encode images into a compact latent space, reducing computational cost but introducing an optimization dilemma: a higher-dimensional latent space improves reconstruction fidelity but often hampers…

Disentangled representations enable models to separate factors of variation that are shared across experimental conditions from those that are condition-specific. This separation is essential in domains such as biomedical data analysis,…

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep…

In this paper we tackle a fundamental question: "Can we train latent diffusion models together with the variational auto-encoder (VAE) tokenizer in an end-to-end manner?" Traditional deep-learning wisdom dictates that end-to-end training is…