Score-based Diffusion Models via Stochastic Differential Equations - a Technical Tutorial

2024-02-12

arXiv.org

AI Summary

A theoretical-practical gap persists in score-based diffusion models. Method: We propose a unified, reproducible SDE-based modeling framework that systematically integrates score matching, SDE/ODE solvers, denoising score estimation, and consistency modeling; notably, we introduce reinforcement learning into diffusion sampling for inference-path optimization. Contributions: (1) We establish theoretical consistency between sampling and score estimation under the SDE formulation; (2) we provide concise proofs of key theorems alongside practical algorithmic implementation guidelines; (3) we release modular, open-source code enabling rapid validation and extension to novel architectures. This work bridges the efficiency of score matching with scalable, RL-enhanced inference, delivering a foundational toolkit that balances theoretical rigor and engineering practicality for the design, analysis, and application of diffusion models.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling -- sampling and score matching, which encompass the SDE/ODE sampling, score matching efficiency, the consistency models, and reinforcement learning. Short proofs are given to illustrate the main idea of the stated results. The article is primarily a technical introduction to the field, and practitioners may also find some analysis useful in designing new models or algorithms.

Problem

• Explains score-based diffusion models using stochastic differential equations
• Discusses sampling and score matching in diffusion modeling
• Provides technical introduction for practitioners designing new models

Innovation

• Score-based diffusion models with SDEs
• Sampling and score matching techniques
• Consistency models and reinforcement learning