Directions

• Most diffusion switching from DDPM to rectified flows, which can converge in fewer steps

Diffusion (DDPM)

Misc background

• the score function (or Fisher score) is defined as the gradient of the log-likelihood $\nabla_x \log p(x)$

Overview

• General concept: each step, add Gaussian noise. Use CNN to recover.

• Train model $\epsilon_\theta$ to predict noise given the noised image and a timestep embedding

  • Conceptually, this model finds the direction to move $x$ to maximize how likely it is an image.

    

• Sampling: at each timestep

  • Predicting fully from noise to initial image doesn’t work well (predicts the mean which is blurry), so move in small steps, which yields better results
  • So subtract the predicted noise, but also add back in some noise (adds stability somehow)

Forward

In one step (the “nice property” of Gaussians/”reparameterization trick”):

Background for reverse

First we need to understand what we’re modeling. It’s the q distribution. Forward is easy. Reverse is intractable: