Probabilistic ML - 21 - Diffusion Models

2025-07-11 · Source: Tübingen Machine Learning - YouTube · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Advanced, extended

Summary

Diffusion Models are introduced as a modern generative modeling technique addressing limitations of traditional Markov Chain Monte Carlo (MCMC) methods, which struggle with complex, multimodal, or manifold-lying probability distributions. The core concept involves a "forward process" that iteratively adds small Gaussian noise to data samples, transforming a complex distribution (like the "two moons" dataset) into a simpler, nearly standard Gaussian one over many steps (e.g., 10,000). The "backward process" reverses this by starting from a standard Gaussian sample and iteratively "denoising" it back to a sample from the original complex distribution. This reversal is achieved by training a deep neural network to predict the noise term at each step, minimizing an L2 loss. This continuous process can be framed as solving a Stochastic Differential Equation (SDE), or more efficiently, an Ordinary Differential Equation (ODE) via probability flow, enabling the generation of high-quality samples from complex data manifolds, as seen in advanced image generation tools.

Key takeaway

For Machine Learning Engineers developing generative models, understanding diffusion processes is crucial for overcoming MCMC limitations in complex data. Your team should explore iterative noise-based approaches, particularly flow matching with ODE solvers, to efficiently generate high-quality samples from multimodal or manifold-lying distributions. Consider conditioning the noise prediction network on additional inputs to enable controlled generation, such as text-to-image synthesis.

Key insights

Diffusion models transform complex distributions into simple Gaussians via iterative noise, then reverse the process to generate data.

Principles

• Convolving with Gaussian noise smooths multimodal distributions.
• Iterative small noise steps enable tractable reversal.
• Learning the noise vector field facilitates backward sampling.

Method

Train a neural network to predict the noise added in a forward diffusion process. Then, use this learned noise predictor to iteratively denoise samples from a standard Gaussian back to the target data distribution.

In practice

• Use AdamW for training diffusion model neural networks.
• Condition generation on inputs (e.g., text) via network input.
• Employ ODE solvers for faster inference in flow matching.

Topics

• Diffusion Models
• Generative Models
• Markov Chain Monte Carlo
• Stochastic Differential Equations
• Probability Flow
• Neural Networks
• Image Generation

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Student

Related on AIssential

• More Than Image Generators: A Science of Problem-Solving using Probability | Diffusion Models — Diffusion models combine deep learning with Langevin sampling to generate images by iteratively following noisy gradients of an image's probability distribution.
• A Unified Approach to Analysis and Design of Denoising Markov Models — A unified mathematical framework rigorously designs and analyzes denoising Markov models, integrating diverse dynamics and objectives.
• A Mathematical Introduction to Diffusion Models — This introduction mathematically grounds diffusion models by tracing sampling dynamics from classical methods to modern samplers.
• Uncertainty Estimation for Molecular Diffusion Models — A post-hoc method estimates per-sample uncertainty in molecular diffusion models, correlating negatively with sample quality.
• Statistical guarantees for denoising reflected diffusion models — Reflected diffusion models provide statistical guarantees for generative AI, resolving unbounded state space issues in implementations.
• Likelihood Matching for Diffusion Models — Likelihood Matching directly optimizes diffusion model training by integrating score and covariance matching via quasi-likelihood.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by Tübingen Machine Learning - YouTube.