Diagram of the probability transition process in speculative sampling.

How is the Speculative Decoding Algorithm Constructed?

A simple mathematical derivation of the algorithm construction process from the paper “Fast Inference from Transformers via Speculative Decoding”.

December 26, 2025 · Updated: December 27, 2025 · 5 min · 884 words · Shichao Song
Diagram of the basic principle of diffusion models, showing recovery of an image from noise. Generated by [Google Nano Banana (gemini-2.5-flash-image-preview)](https://www.nano-banana.ai/)

Fully Annotated Guide to "What are Diffusion Models?"

Diffusion models are the de facto standard for image generation. Lilian Weng’s “What Are Diffusion Models?” is an excellent introduction to it, but readers without a solid mathematical background may struggle. This article fills that gap with clear, step‑by‑step derivations and explanations.

September 2, 2025 · 74 min · 15730 words · Shichao Song