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We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary time-dependent stochasticity parameter or a probability flow ODE, corresponding…
Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…
We provide attainable analytical tools to estimate the error of flow-based generative models under the Wasserstein metric and to establish the optimal sampling iteration complexity bound with respect to dimension as $O(\sqrt{d})$. We show…
An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed. We first utilize the Cram\'er-Rao bound to identify the Gaussian setting as a fundamental…
To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the…
Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…
The diffusion model has shown remarkable success in computer vision, but it remains unclear whether the ODE-based probability flow or the SDE-based diffusion model is more superior and under what circumstances. Comparing the two is…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
Score-based generative models have emerged as a powerful approach for sampling high-dimensional probability distributions. Despite their effectiveness, their theoretical underpinnings remain relatively underdeveloped. In this work, we study…
Score-based generative modeling with probability flow ordinary differential equations (ODEs) has achieved remarkable success in a variety of applications. While various fast ODE-based samplers have been proposed in the literature and…
Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
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…
Statistical surrogate modeling of fluid flows is hard because dynamics are multiscale and highly sensitive to initial conditions. Conditional diffusion surrogates can be accurate, but usually need hundreds of stochastic sampling steps. We…
Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these,…
Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic…
Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…
Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…