Understanding Diffusion Models via Code Execution

TL;DR

This paper provides a concise, implementation-focused explanation of diffusion models, bridging the gap between theoretical formulations and practical code through a minimal, understandable example.

Contribution

It introduces a simplified, 300-line code implementation that clarifies how diffusion models operate in practice, connecting theory with actual code execution.

Findings

Provides a minimal, understandable diffusion model implementation

Clarifies the relationship between mathematical theory and code

Offers accessible resources for researchers to learn diffusion models

Abstract

Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.