[Paper Review] Diffusion Models: A Comprehensive Survey of Methods and Applications

L. Yang, Zhilong Zhang+7 more|arXiv (Cornell University)|Sep 2, 2022

Mathematical Biology Tumor GrowthMathematics150 citations

TL;DR

A comprehensive survey of diffusion models that catalogs foundations, efficient sampling, likelihood improvements, and handling of data with special structures, and surveys connections to other generative models and broad applications.

ABSTRACT

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

Motivation & Objective

• Provide a structured overview of diffusion model foundations (DDPMs, SGMs, Score SDEs) and their connections.
• Categorize recent work into efficient sampling, improved likelihood, and data with special structures.
• Review how diffusion models combine with other generative models (VAEs, GANs, normalizing flows, autoregressive, EBMs).
• Survey broad applications across vision, NLP, temporal data, multi-modal tasks, and interdisciplinary domains.

Proposed method

• Explain three main formulations: DDPMs, SGMs, and Score SDEs and their unifying perspective.
• Describe training via variational lower bound (VLB) and score-matching objectives.
• Discuss sampling methods including annealed Langevin dynamics, SDE/ODE solvers, and predictor-corrector schemes.
• Present optimization techniques such as noise schedule design, reverse variance learning, and exact likelihood considerations.
• Outline efficient sampling categories: learning-free sampling and learning-based sampling (discretization, distillation, truncated diffusion).
• Summarize connections to VAEs, GANs, normalizing flows, autoregressive models, and EBMs.

Experimental results

Research questions

• RQ1 What are the foundational formulations of diffusion models and how do they relate (DDPMs, SGMs, Score SDEs)?
• RQ2 How can diffusion models be made faster and more sample-efficient without sacrificing quality?
• RQ3 How can diffusion models be adapted to improve likelihood estimation and handle data with special structures (discrete, manifold, invariant)?
• RQ4 How do diffusion models connect to and benefit from integration with other generative model families (VAEs, GANs, flows, autoregressive, EBMs)?
• RQ5 What are the broad application domains where diffusion models have the most impact and potential future directions?

Key findings

• Diffusion models have emerged as state-of-the-art in image synthesis and show potential across video, molecules, and other domains.
• The survey categorizes advances into efficient sampling, improved likelihood, and handling data with special structures.
• There is potential for combining diffusion models with other generative models to achieve stronger performance.
• The paper surveys a wide range of applications from computer vision to natural language processing, temporal data, and interdisciplinary fields.
• It provides a unifying perspective by showing how DDPMs, SGMs, and Score SDEs can be reduced to one another under a common diffusion framework.