Neelay Ranjan
energy-based models · diffusion · flight-path generation
Illustrative Langevin simulation. Particles descend an energy landscape carved from the letterforms. Thermal kicks knock them out of the wells; they re-anneal back into them, and follow you down the page as you scroll. Drag to pick up a cluster. Hand-built landscape, not a trained model.
NASA Ames · Regenstrief Institute
DDPM vs. flow matching. Both learn to turn noise into data, but they take different routes there. A diffusion model (DDPM) reverses a stochastic noising process: sampling is a random walk that removes a little noise at each of many steps, so the path from noise to sample is jagged and takes a different route every run. Flow matching instead learns a velocity field and follows it as a deterministic ODE. The trajectory is smooth, repeatable, and much straighter, which is why it can sample in far fewer steps. Straighten the paths further (rectified flow / reflow) and they approach straight line segments, collapsing dozens of steps into a handful.
The panels above are illustrative: hand-drawn fields on a 2D toy distribution, not a trained model. In two dimensions these trajectories can be made genuinely real; in the high-dimensional space of actual image models the same picture becomes a projection.