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Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large…

Diffusion models, which have been advancing rapidly in recent years, may generate samples that closely resemble the training data. This phenomenon, known as memorization, may lead to copyright issues. In this study, we propose a method to…

Out-of-distribution (OOD) detection is essential for reliable deployment of machine learning systems in vision, robotics, reinforcement learning, and beyond. We introduce Score-Curvature Out-of-distribution Proximity Evaluator for Diffusion…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

There has been a flurry of activity around using pretrained diffusion models as informed data priors for solving inverse problems, and more generally around steering these models using reward models. Training-free methods like diffusion…

Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…

Diffusion models have gained prominence in generating high-quality sequences of text. Nevertheless, current approaches predominantly represent discrete text within a continuous diffusion space, which incurs substantial computational…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

Diffusion models have made remarkable progress in solving various inverse problems, attributing to the generative modeling capability of the data manifold. Posterior sampling from the conditional score function enable the precious data…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…

Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

We consider statistical tasks in high dimensions whose loss depends on the data only through its projection into a fixed-dimensional subspace spanned by the parameter vectors and certain ground truth vectors. This includes classifying…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Diffusion and flow-based models are ubiquitously used for generative modelling and density estimation. They admit a deterministic probability flow ordinary differential equation (PF-ODE), analogous to continuous normalizing flows (CNFs),…

Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

In programming, learning code representations has a variety of applications, including code classification, code search, comment generation, bug prediction, and so on. Various representations of code in terms of tokens, syntax trees,…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…