Consistency models

Abstract

• Support fast one-step generation by design, while still allowing multistep sampling to trade compute for sample quality
• trained either by distilling pre-trained diffusion models, or as standalone generative models altogether
• They build on top of the probability flow (PF) ordinary differential equation (ODE) in continuous-time diffusion models, whose trajectories smoothly transition the data distribution into a tractable noise distribution. We propose to learn a model that maps any point at any time step to the trajectory’s starting point.
  • self-consistency property: Points on the same trajectory map to the same initial point
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Main idea

• A trained diffusion model, one way or another, estimates the score function of the probability distribution
  • whether that’s done directly through score matching
  • or through denoising objective, where in practice, $\nabla p(x_t)=-\alpha {ϵ}_0$
    • where ${ϵ}_0$ is the source noise i.e. $x_t=x_0+{ϵ}_0$
• As soon as you have the score function, assuming it’s a Gaussian Diffusion model, you can sample trajectories from pure noise $x_T$ to new “clean” samples ${\hat{x}}_0$, using an ODE solver (e.g. Euler).
• Then you can enforce the objective that any samples on a trajectory should be mapped back to ${\hat{x}}_0$.