Running the Heat Equation Backwards: Diffusion Models and Flow Matching

Deep End Era. Engineering with Sankalp · Oct 12, 2026 · 1h 7m

Pipeline integrity engineer Wren Okafor watches a dye pulse smear out in a water line, and her friend Teodor Lindqvist, a machine learning engineer, claims his whole field runs that smearing backwards. Starting from the score (the gradient of log density, which makes the normalising constant vanish), the episode builds Langevin dynamics, Song and Ermon's annealed noise-conditional score networks, and Ho, Jain and Abbeel's DDPM (2020): the variance-preserving forward process, the noise-prediction loss, and its equivalence to denoising score matching. It then covers the score-SDE view (Song et…