Related papers: Minimax Optimality of the Probability Flow ODE for…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…
Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…
Diffusion models have emerged as a powerful framework in generative modeling, typically relying on optimizing neural networks to estimate the score function via forward SDE simulations. In this work, we propose an alternative method that is…
Despite the widespread adoption of deterministic samplers in diffusion models (DMs), their potential limitations remain largely unexplored. In this paper, we identify collapse errors, a previously unrecognized phenomenon in ODE-based…
Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by…
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…
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…
We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…
A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through…