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Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of…
Large-scale generative models, such as text-to-image diffusion models, have garnered widespread attention across diverse domains due to their creative and high-fidelity image generation. Nonetheless, existing large-scale diffusion models…
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 emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…
Dataset distillation provides an effective approach to reduce memory and computational costs by optimizing a compact dataset that achieves performance comparable to the full original. However, for large-scale datasets and complex deep…
Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…
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…
Domain generalization (DG) for object detection aims to enhance detectors' performance in unseen scenarios. This task remains challenging due to complex variations in real-world applications. Recently, diffusion models have demonstrated…
Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Due to the inherent property of diffusion models, most existing methods…
For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of approximation schemes based on differencing and interpolation. As opposed to classical numerical methods, these schemes work for general…
The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
This paper introduces $\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has…