Score-Based Generative Modeling through Stochastic Differential Equations

Inside the paper

The problem

Noise-based generative models had shown promising image results, but their discrete noise schedules and sampling methods were often presented separately. The authors investigate what becomes possible when the noise process is described continuously in time.

The idea

A stochastic differential equation describes how data become noise, and a learned score field supplies the information needed to run a corresponding process backward. Different numerical solvers then provide different ways to sample from the model.

How it works

• Choose a forward process that gradually perturbs data until its distribution approaches a tractable noise distribution.
• Train a time-dependent network to estimate the score, the gradient of the log density, at different stages of perturbation.
• Start from noise and numerically solve the reverse-time equation using the estimated score to generate a sample.
• A predictor-corrector sampler combines numerical steps with score-based corrections, while a related ordinary differential equation provides a deterministic path and likelihood computation.

What it showed

The paper compares solvers and reports image generation and likelihood results on CIFAR-10. It also demonstrates conditional generation and image restoration tasks, including inpainting and colorization, using its score-based framework.

Read it for

Figure 2 and Sections 3.1–3.3 introduce the forward process, learned score and reverse process. Continue to Sections 4 and 5 for samplers and experiments; the extended derivations in the appendices can be read later.

Written in our own words from the paper itself. A draft the editors have not yet reviewed.