Forward and Reverse Diffusion

Training destroys images and learns to predict the noise; sampling runs the destruction backwards

Forward and Reverse Diffusion Training destroys images and learns to predict the noise; sampling runs the destruction backwards 01 / Pixel / data space 02 / Diffusion chain (fixed) 03 / Denoiser network (learned) 04 / Training objective Forward: training time Reverse: sampling time Clean image · x_0 dataset · Pixel / data space › Forward: training time Clean image x_0 dataset Jump to t · closed-form · Diffusion chain (fixed) › Forward: training time Jump to t closed-form Predict noise · from x_t and t · Denoiser network (learned) › Forward: training time Predict noise from x_t and t MSE loss · vs true noise · Training objective › Forward: training time MSE loss vs true noise Pure static · x_T ~ N(0,I) · Diffusion chain (fixed) › Reverse: sampling time Pure static x_T ~ N(0,I) Predict noise · same network · Denoiser network (learned) › Reverse: sampling time · CFG here Predict noise same network CFG here Step to t-1 · sampler · Diffusion chain (fixed) › Reverse: sampling time · repeat Step to t-1 sampler repeat Generated · new image · Pixel / data space › Reverse: sampling time Generated new image noisy x_t true noise t = 0 same weights Legend User UI Agent logic Policy Tool action Context / trace

Forward (fixed)

  • • A Markov chain of Gaussian corruptions
  • • Closed form jumps to any step in one draw
  • • No learned parameters anywhere

Reverse (learned)

  • • Small Gaussian steps reverse as Gaussians
  • • Generation = regression, iterated
  • • ~20-1000 network calls per image

The trade

  • • Stable MSE training, no adversary
  • • Full mode coverage from likelihood
  • • Price paid in sampling steps

Workflow diagram • Built with Archify • Create yours ↗ • Hover to trace • R route • Click to focus • +/− zoom • M radar • [/] views • P play story • T theme • E export