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Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and…
Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its acquisition, the approximated score function is then…
We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is…
Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean…
Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…
We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as…
We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward…
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,…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…