Interactive · Three Dynamics, One Shared Marginal pₜ

The forward process defines a family of marginals pₜ. Three dynamics all produce this same pₜ at every t, but flow in different directions. Drag the slider: moving rightward (t↑) lights up the forward process and forward PF-ODE (data→noise). Moving leftward (t↓) lights up the reverse SDE and reverse PF-ODE (noise→data). The PF-ODE works both ways — it is the only dynamics that is reversible in time.

data (t=0)   ← time t = 0.50 →   noise (t=1)
drag slider
Drag the slider to see which dynamics are active in each direction. The PF-ODE (bottom) lights up in both directions.