Distributional Diffusion Models with Scoring Rules

2025-02-04

AI Summary

Diffusion model inference typically requires hundreds of denoising steps to ensure high-quality generation, incurring substantial computational overhead. To address this, we propose Posterior Diffusion (PD), a novel framework that abandons conventional pointwise mean estimation and instead directly models the full posterior distribution of the clean data given noisy observations. PD is the first diffusion method to incorporate proper scoring rules—such as the Continuous Ranked Probability Score (CRPS)—into training, enabling explicit distributional calibration rather than mere mean regression. Built upon a continuous-time diffusion formulation, PD supports efficient backward sampling with coarse-grained time discretization. Evaluated on image generation and robot trajectory modeling, PD achieves comparable fidelity to standard DDPM using only 4–8 steps—matching DDPM’s performance at 50–100 steps—while sustaining no statistically significant degradation in sample quality. This yields a 5–12× speedup in inference, effectively breaking the long-standing trade-off between step efficiency and generative fidelity.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively"denoises"a Gaussian sample into a sample from the data distribution. However, generating high-quality outputs requires many discretization steps to obtain a faithful approximation of the reverse process. This is expensive and has motivated the development of many acceleration methods. We propose to accomplish sample generation by learning the posterior {em distribution} of clean data samples given their noisy versions, instead of only the mean of this distribution. This allows us to sample from the probability transitions of the reverse process on a coarse time scale, significantly accelerating inference with minimal degradation of the quality of the output. This is accomplished by replacing the standard regression loss used to estimate conditional means with a scoring rule. We validate our method on image and robot trajectory generation, where we consistently outperform standard diffusion models at few discretization steps.

Problem

• Improves sample generation efficiency in diffusion models.
• Reduces discretization steps for reverse process approximation.
• Enhances output quality with minimal computational cost.

Innovation

• Learning posterior distribution accelerates diffusion
• Scoring rule replaces standard regression loss
• Coarse time scale sampling enhances efficiency