Core Principles and Mathematical Foundations of Diffusion Models
By
Anon84
Crispy enough to crunch, soft enough to enjoy. A good bake.
Summary
This monograph presents the core principles of diffusion models, explaining how they work through three complementary mathematical perspectives: variational (learning to remove noise step by step), score-based (learning the gradient of data distribution), and flow-based (treating generation as following a smooth path from noise to data). The text traces the origins of diffusion models, showing how diverse formulations arise from shared mathematical ideas, and discusses applications like controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models.
Key quotes
· 4 pulledDiffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions.
The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution.
These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data.
It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.
You might also wanna read
What pretraining on unlabeled text teaches large language models about language structure
Pretraining on unlabeled text teaches large language models to model the statistical structure of language by optimizing next-token predicti
sebastianraschka.com·1d ago
AI and Publish-or-Perish Culture Are Overwhelming Academic Peer Review, Study Finds
This article, authored by the AI Task Force for Organization Science, examines how generative AI is reshaping academic peer review and resea
AI-generated research papers overwhelm academic peer review and citation systems
The article discusses a growing crisis in academic publishing where AI-generated research papers are flooding journals and citation database
The Verge·16d ago
Decoding AI's Internal Language: How Sparse Autoencoders Help Interpret Neural Activations
This article discusses how AI models like Claude process language through numerical activations, similar to neural activity in the human bra
anthropic.com·24d ago
Study Reveals Convergent Evolution in How Language Models Learn Number Representations
This research paper investigates how different language models (Transformers, Linear RNNs, LSTMs, and classical word embeddings) learn to re
arxiv.org·1mo agoHow Large Language Models Work: A Visual Deep Dive into Training Data Collection
This article provides a visual deep dive into how Large Language Models (LLMs) work, starting with the data collection process. It explains