Published in arxiv, 2025
This paper studies the generalization property of diffusion models through the lens of statistical learning. We develop a perspective that enables using existing tools to characterize the generalization ability of these generative models.
Published in ICML 2025, 2025
This paper introduces a novel framework for discrete data generation on the hypercube ${0, 1}^d$. We establish theoretical and methodological alignment with classical continuous score-based modesls. We demonstrate the effectiveness of this approach on low and high dimensional datasets (Binary MNIST), beating other state-of-the-art methods like Discrete Flow Matching
Published in ICLR 2025, 2025
This paper introduces a novel framework to use heavy-tailed noise in the denoising diffusion paradigm, which constitutes a generalization of the original DDPM method. Using heavy-tailed noise is shown to bring benefits in various contexts: heavy-tailed data distributions, better robustness to class imbalance, and smaller computational time.
Published in NeurIPS 2024, 2024
We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), which combine deterministic motion with random jumps. Like diffusions, PDMPs can be reversed in time. We derive explicit expressions for jump rates and kernels in the time-reversed processes and propose efficient training methods and approximate simulation techniques. Additionally, we provide bounds on the total variation distance between the data and model distributions, supported by promising numerical simulations.