AI researcher proposes x0 velocity, a new training target for flow-matching diffusion models
ostrisai · x · 2026-10-22
Image-model trainer ostris proposes "x0 velocity," a new regression target for flow-matching diffusion models.
- Keeps the forward process and sampling trajectory identical to flow matching: the network output converts back to a velocity with one subtraction, so any existing sampler, scheduler, or guidance method runs unchanged
- Only the target changes: target = clean + (1-t)(clean-noise) — plain x0 prediction at the pure-noise end, and x0 extrapolated one unit along the flow line elsewhere
- Unlike x0 prediction, the correction magnitude stays constant across timesteps (x0's shrinks to zero, starving fine-detail steps); unlike velocity prediction, the output is always image-shaped, and the loss equals the flow-matching velocity loss, so no timestep weighting is needed
- Author reports more stable training, better tolerance of high-frequency content, enabling more latent channels and deeper compression
An attached chart compares input/target MSE across sigmas for all three targets on the same noise sample.
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