Diffusion from noise to data

Watch noise turn into a 2D dataset using the exact reverse diffusion process, with the score field drawn as arrows.

AdvancedExplained in Diffusion: from noise to data

Diffusion on a 2D dataset

Dots are samples. Blue shading is the noisy data density at time t; arrows show its score, the direction toward higher density.

Direction
Dataset
Sampler
t = 1.000
Time t1.000
Signal kept, sqrt(abar)0.007
Noise, sqrt(1 - abar)1.000

Try this

  • Press Denoise and watch when the shape actually appears. Most of the structure arrives in the last part of the run.
  • Switch between Deterministic (ODE) and Random (SDE) and replay. Both match the data; only the paths differ.
  • Choose Add noise and scrub: every dataset becomes the same round cloud.

The data here is a mixture of Gaussian blobs, so the score of every noisy version is known exactly. Real diffusion models learn an approximation of it with a neural network.

Try "embedding", "softmax", "overfitting", or "backpropagation".