Prediction Target Parameterization

The choice of whether a diffusion model's network should output noise, velocity, or the clean data itself.

When training a diffusion or flow-matching model, clean data x0 is first noised into x_t, and the network, seeing x_t, has to output some quantity to compute the loss against — there are several choices for what that quantity should be. ε-prediction has the network guess the noise that was added, which is what 2020's DDPM does; x0-prediction guesses the clean data directly; v-prediction, proposed by Salimans and Ho in 2022, predicts a weighted combination of noise and data, and is more stable with very few sampling steps; the velocity field predicted in flow matching and rectified flow also falls into this category. Given x_t and the timestep, the three are mathematically interconvertible, but they differ in how hard they are to train, how errors get weighted across noise levels, and how well they work with few sampling steps. A 2025 paper by Tianhong Li and Kaiming He, JiT, argues that predicting the clean data directly in high-dimensional pixel space is easier to learn than predicting noise or velocity. In robotics, Diffusion Policy defaults to ε-prediction, while flow-matching VLAs like π0 predict velocity.

ExampleDiffusion Policy's noise-prediction network ε_θ takes a noised action sequence as input and outputs the estimated noise; π0's action expert instead outputs a velocity vector, and at deployment integrates 10 steps starting from pure noise to get an action chunk.

Also called

ε-prediction, v-prediction, x0-prediction

Related

Diffusion Model · Flow Matching · Rectified Flow · Denoising Diffusion Probabilistic Model · Velocity Field · Denoising Loss (Diffusion Loss)

Sources

Denoising Diffusion Probabilistic Models (DDPM, arXiv 2006.11239)
Progressive Distillation for Fast Sampling of Diffusion Models (v-prediction, arXiv 2202.00512)
Back to Basics: Let Denoising Generative Models Denoise (JiT, arXiv 2511.13720)

As of

2025-11