Denoising Loss (Diffusion Loss)

A diffusion model's training objective: add noise to clean data and have the network predict exactly the noise that was added.

Denoising loss is the loss function used to train diffusion models; its most common form comes from Ho, Jain, and Abbeel's 2020 DDPM paper: pick a random noising step t, mix Gaussian noise into a real sample according to a noise schedule, and have the network predict the added noise from the noisy sample and t, with the loss being the mean squared error between predicted and true noise. The paper calls this the simplified objective, L_simple; it's a weighted form of the variational lower bound and corresponds to denoising score matching, and in practice it produces better generation quality than optimizing the full lower bound directly. The network can instead be reparameterized to predict the clean sample x0 or a velocity term v — different prediction-target parameterizations. In robotics, Diffusion Policy treats an action sequence as the data to generate, conditioned on observations, and trains it with the same noise-prediction mean squared error; flow-matching models like π0 use a similarly-shaped flow-matching loss instead.

ExampleTraining Diffusion Policy: take a snippet of future actions from a demonstration, pick a random noise step and add noise to it; the network looks at the current camera image and the noisy actions and outputs what it thinks the added noise was, and the mean squared error against the true noise is backpropagated.

Also called

Diffusion Loss, Noise-Prediction Loss, L_simple

Related

Diffusion Model · Denoising Diffusion Probabilistic Model · Noise Schedule · Prediction Target Parameterization · Flow Matching Loss · Diffusion Policy

Sources

Denoising Diffusion Probabilistic Models (arXiv 2006.11239)
Diffusion Policy: Visuomotor Policy Learning via Action Diffusion (arXiv 2303.04137)