Design axis
Objective
What is the model trained to predict — noise, velocity, or the next token?
Diffusion-loss autoregression
Autoregress over a sequence of continuous tokens, using a small per-token diffusion model as the loss instead of a categorical cross-entropy over a codebook.
Diffusion (epsilon/v/x0-prediction)
Learn to reverse a fixed noising process by predicting the noise, velocity, or clean signal at each step (DDPM-style).
Drifting field
Learn the generator mapping itself and evolve its pushforward distribution during training until it matches the data, rather than learning a score or velocity to integrate at sampling time.
Flow matching / rectified flow
Directly regress the velocity field of a (near-)straight path between a noise sample and a data sample, rather than reversing a stochastic noising process.
Stochastic interpolant framework
A generalized formulation that treats diffusion and flow matching as two points in a continuous family of interpolants between noise and data, exposing objective/coupling/sampler as independent design choices.
Average (mean) velocity
Regress the average velocity over a finite interval instead of the instantaneous velocity, which yields a self-contained identity that supports one-step sampling.
Next-scale autoregression
Predict an image as a sequence of token maps at increasing resolution, each conditioned on all coarser scales, instead of raster-order next-token prediction.
Normalizing flow
An invertible mapping trained by exact maximum likelihood, giving exact densities and an inverse for free at the cost of architectural constraints.
Transition matching
Model generation as a sequence of discrete-time Markov transition kernels over a continuous state, which subsumes both flow matching and continuous-token autoregression as special cases.