Related papers: When Diffusion Model Can Ignore Dimension: An Entr…
Diffusion models excel at capturing complex data distributions, such as those of natural images and proteins. While diffusion models are trained to represent the distribution in the training dataset, we often are more concerned with other…
Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. Such information is coined as guidance. For example, in text-to-image synthesis, text…
Diffusion models are often trained in low-dimensional latent spaces, which are then reused for related but shifted datasets. In this work, we study when such latent reuse remains reliable under distribution shift. We consider a…
Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of…
Diffusion models have become a standard approach for generative modeling in continuous domains, yet their application to discrete data remains challenging. We investigate why Gaussian diffusion models with the DDPM solver struggle to sample…
Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…
In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress…
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…
Compression has been a critical lens to understand the success of Transformers. In the past, we have typically taken the target distribution as a criterion to evaluate a model's compression performance. Nevertheless,it often remains…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
While perspective is a well-studied topic in art, it is generally taken for granted in images. However, for the recent wave of high-quality image synthesis methods such as latent diffusion models, perspective accuracy is not an explicit…
The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex…
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge…
Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…
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…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking.…
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional…
Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…