Analytic Understanding of Diffusion Models

Join us: Analytic Diffusion Social — an informal gathering 5–7 PM on June 4, right after the tutorial, on the terrace outside the Bluebird Ballroom (3rd floor).

RSVP on Luma

New: We are releasing Analytic Diffusion Studio — a unified framework for training-free analytical diffusion models.

View on GitHub

Schedule

The tutorial runs for a full day and combines lectures with interactive hands-on sessions.

Morning Session — 8:30 – 12:00

8:30 – 9:10	Intro + notations by Artem, Chris Slides
9:10 – 9:20	Coffee Break
9:20 – 10:30	What is the optimal denoiser? What is the impact of smoothing? by Chenyang, Chris Slides Colab: Optimal denoiser Colab: Smoothing
10:30 – 10:50	Coffee Break
10:50 – 12:00	How far can the linear perspective get us? by Binxu Slides Colab

12:00 – 13:30

Lunch Break

Afternoon Session — 13:30 – 17:00

13:30 – 14:30	Seeing generalization through locality by Mason Slides Colab
14:30 – 14:40	Coffee Break
14:40 – 15:10	Why do diffusion models learn to be local? by Artem Slides Colab
15:10 – 15:20	Coffee Break
15:20 – 16:00	How do diffusion models learn and encode global structures? by Zahra Slides
16:00 – 16:10	Coffee Break
16:10 – 17:00	Open question in the field + Q&A by Artem, Chenyang, Chris, Binxu, Mason, Zahra
17:00 – 19:00	Analytic Diffusion Social An informal gathering to chat about analytic diffusion models, right after the tutorial. On the terrace outside the Bluebird Ballroom (3rd floor, west-most side of the terrace). RSVP on Luma

Overview

Denoising diffusion models have achieved state-of-the-art results for generative modeling across images, video, and audio. Yet analysis of the training objective reveals a paradox: the objective admits a unique closed-form solution that is a function of the training data alone—and this solution can only reproduce training examples, exhibiting perfect memorization.

How, then, do deep diffusion models generalize? This tutorial explores the emerging family of analytical diffusion models that shed light on this question. Starting from the fundamentals, we build toward the current understanding of generalization mechanisms—score smoothing, inductive biases of neural architectures, training dynamics, and data geometry—all through the lens of optimal denoising.

The tutorial combines lectures with hands-on Jupyter notebook sessions so that attendees can run experiments, probe the theory, and build intuition firsthand.

Full day (8:30 AM – 5:00 PM)

6 speakers

Hands-on notebook sessions

For researchers with ML background

Speakers

Artem Lukoianov

MIT CSAIL

PhD student, author of “Locality in Image Diffusion Models Emerges from Data Statistics” (Spotlight, NeurIPS 2025).

Chenyang Yuan

Toyota Research Institute

Research Scientist and creator of smalldiffusion, an open-source library for controlled diffusion experiments.

Christopher Scarvelis

MIT CSAIL, Rutgers University

Incoming Assistant Professor, Rutgers University and author of “Closed-Form Diffusion Models” (TMLR, 2025).

Mason Kamb

Stanford University

PhD student and first author of “An Analytic Theory of Creativity in Convolutional Diffusion Models” (ICML 2025, Oral).

Binxu Wang

Harvard Kempner Institute

Research Fellow studying the intersection of generative models and visual neuroscience; incoming Group Leader at Janelia and author of “The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models” (TMLR 2024).

Zahra Kadkhodaie