Related papers: Stochastic interpolants with data-dependent coupli…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The goal of a generative model is to capture the distribution underlying the data, typically through latent variables. After training, these variables are often used as a new representation, more effective than the original features in a…
We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT). The interpolant framework, which allows for connecting two distributions in a more flexible way than…
We explore the usage of meta-learning to derive the causal direction between variables by optimizing over a measure of distribution simplicity. We incorporate a stochastic graph representation which includes latent variables and allows for…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…
In generative models, two paradigms have gained attraction in various applications: next-set prediction-based Masked Generative Models and next-noise prediction-based Non-Autoregressive Models, e.g., Diffusion Models. In this work, we…
Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
Wall-bounded turbulent flows are chaotic and multiscale, rendering real-time prediction at high Reynolds numbers computationally prohibitive in applications such as wind farms. Classical data assimilation methods are based on repeated…
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…
Single-cell gene expression measurements encode variability spanning molecular noise, cell-to-cell heterogeneity, and technical artifacts. Mechanistic stochastic models provide powerful approaches to disentangle these sources, yet inferring…
We develop a new framework for learning variational autoencoders and other deep generative models that balances generative and discriminative goals. Our framework optimizes model parameters to maximize a variational lower bound on the…
Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images…
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…