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Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…
Diffusion models deliver state-of-the-art generative performance across diverse modalities but remain computationally expensive due to their inherently iterative sampling process. Existing training-free acceleration methods typically…
We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…
Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based…
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…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
This paper investigates score-based diffusion models when the underlying target distribution is concentrated on or near low-dimensional manifolds within the higher-dimensional space in which they formally reside, a common characteristic of…
As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…
Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models.…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…
Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify…
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…
Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…
Diffusion models play a pivotal role in contemporary generative modeling, claiming state-of-the-art performance across various domains. Despite their superior sample quality, mainstream diffusion-based stochastic samplers like DDPM often…
Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. In this paper, we revisit the diffusion sampling process and identify a fundamental cause of sample quality…
Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension,…
Diffusion probabilistic models (DPMs) have been shown to generate high-quality images without the need for delicate adversarial training. However, the current sampling process in DPMs is prone to violent shaking. In this paper, we present a…