Related papers: Lipschitz Singularities in Diffusion Models
Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…
The diffusion model has recently emerged as a potent approach in computer vision, demonstrating remarkable performances in the field of generative artificial intelligence. Capable of producing high-quality synthetic images, diffusion models…
In Lipschitz domains, we study a Darcy-Forchheimer problem coupled with a singular heat equation by a nonlinear forcing term depending on the temperature. By singular we mean that the heat source corresponds to a Dirac measure. We establish…
Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…
Diffusion models (DMs) have been significantly developed and widely used in various applications due to their excellent generative qualities. However, the expensive computation and massive parameters of DMs hinder their practical use in…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
Latent diffusion models achieve state-of-the-art performance on a variety of generative tasks, such as image synthesis and image editing. However, the robustness of latent diffusion models is not well studied. Previous works only focus on…
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…
Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs)…
Diffusion Models (DMs) iteratively denoise random samples to produce high-quality data. The iterative sampling process is derived from Stochastic Differential Equations (SDEs), allowing a speed-quality trade-off chosen at inference. Another…
In this paper, we study the Lipschitz continuous dependence of conservative H\"older continuous weak solutions to a variational wave system derived from a model for nematic liquid crystals. Since the solution of this system generally forms…
We study stability, long-time behavior and moment estimates for stochastic evolution equations with additive Wiener noise and with singular drift given by a divergence type quasilinear diffusion operator which may not necessarily exhibit a…
Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard…
Diffusion-based models have shown great promise in molecular generation but often require a large number of sampling steps to generate valid samples. In this paper, we introduce a novel Straight-Line Diffusion Model (SLDM) to tackle this…
Existence, uniqueness, and $L_p$-approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients…
The Diffusion Transformer (DiT) architecture is the state-of-the-art paradigm for high-fidelity image generation, underpinning models like Stable Diffusion-3 and FLUX.1. However, deploying these models on resource-constrained mobile devices…
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a…
We introduce Efficient Motion Diffusion Model (EMDM) for fast and high-quality human motion generation. Current state-of-the-art generative diffusion models have produced impressive results but struggle to achieve fast generation without…
The Stable Diffusion Model (SDM) is a popular and efficient text-to-image (t2i) generation and image-to-image (i2i) generation model. Although there have been some attempts to reduce sampling steps, model distillation, and network…
We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs…