Understanding Diffusion Models via Code Execution

2025-12-08

AI Summary

Diffusion models exhibit theoretical complexity, and existing tutorials emphasize mathematical derivations without clear mapping to practical implementation. To address this, we propose a minimal, pedagogically focused PyTorch implementation—under 300 lines—that systematically dissects forward diffusion, reverse sampling, noise prediction networks, and the training loop from an execution-centric perspective. For the first time, this compact, fully functional codebase precisely realizes core algorithms—including DDPM, DDIM, and classifier-free guidance—line-by-line. The implementation prioritizes readability and instructional utility, accompanied by open-sourced code and pre-trained models. This significantly lowers barriers to understanding, reproduction, and rapid prototyping. The framework has been widely adopted in academic instruction and research prototyping.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: (Large) Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Bridging theory-practice gap in diffusion models
• Providing code-execution perspective for understanding
• Simplifying implementation to clarify essential components

Innovation

• Concise 300-line code implementation
• Focus on code execution perspective
• Minimal example with essential components