---
title: "Denoising Diffusion Probabilistic Models"
description: "DDPM made diffusion models practical for high-quality image synthesis: corrupt data with a fixed Gaussian chain, train one time-conditioned U-Net to predict the added noise, then reverse the chain from pure noise. Follow the closed-form training shortcut, the simplified objective, and the evidence behind the paper's sample-quality claims."
canonical_url: "https://fanout.sh/daily/2026-10-29-denoising-diffusion-probabilistic-models"
md_url: "https://fanout.sh/daily/2026-10-29-denoising-diffusion-probabilistic-models.md"
last_updated: "2026-10-29"
access: "public"
---

# Denoising Diffusion Probabilistic Models

DDPM made diffusion models practical for high-quality image synthesis: corrupt data with a fixed Gaussian chain, train one time-conditioned U-Net to predict the added noise, then reverse the chain from pure noise. Follow the closed-form training shortcut, the simplified objective, and the evidence behind the paper's sample-quality claims.

## Paper details

- Authors: Jonathan Ho, Ajay Jain, Pieter Abbeel

- Venue: NeurIPS 2020

- Track: AI Research

- Difficulty: Hard

- Reading time: 13 min

- Original paper: https://arxiv.org/abs/2006.11239v2

## What you will learn

- How a closed-form forward marginal lets training jump directly to any noise level instead of simulating every earlier corruption step.

- Why predicting injected noise turns the reverse-process objective into a simple denoising regression problem across timesteps.

- What the CIFAR-10 ablations establish about the simplified objective, and why 1,000-step sampling remained the central cost.

## Continue exploring

[Compare continuous flows](https://fanout.sh/daily/2026-10-01-flow-matching-generative-modeling): Contrast DDPM's stochastic discrete-time reversal with flow matching's learned continuous vector field and ODE-style transport.

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