Gaussian Diffusion Forward Process
Watch signal shrink and Gaussian uncertainty grow in a deterministic diffusion experiment.
Free theory articleWatch signal shrink and Gaussian uncertainty grow in a deterministic diffusion experiment.
Concept & interpretation
The forward noising process in diffusion models incrementally adds Gaussian noise to an initial clean signal x_0 . By fixing a variance schedule βt , we can compute the distribution at any timestep t in a single closed-form step without simulating intermediate steps.
Experiment
Observe the deterministic forward process using the module at https://riano.app/module/gaussian-diffusion-forward-process.
- Set the Clean point to "Axis" (x0=2, y0=0), Beta to "0.1", Steps to "0", and Noise draw to "Diagonal". The variance is 0, giving an infinite SNR. The conditional mean exactly overlaps the sample at (2.0, 0.0).
- Change Steps to "2". Notice the mean shrinks toward the origin at (1.8, 0.0), and the green covariance ellipse grows. The sample jumps diagonally from the mean by the standard deviation.
- Change Steps to "6". The signal shrinks further to mean x = 1.458. The variance per coordinate grows to roughly 0.468, drastically reducing the SNR to roughly 1.134.