You don't need the full corruption path. You need its snapshots.
Generalized Discrete Diffusion from Snapshots (arXiv:2603.21342): discrete diffusion models — which corrupt and reconstruct data in finite state spaces (text, molecular structures, categorical data) — traditionally require tracking the full forward corruption process. GDDS replaces the full path with snapshots: latent states sampled at discrete times along the corruption trajectory. The simplified ELBO derived from snapshots rather than paths enables efficient training with flexible corruption dynamics.
The flexibility matters. Standard discrete diffusion constrains the corruption to specific noise schedules — typically uniform or absorbing. GDDS uses uniformization to separate the corruption rate from the corruption dynamics, allowing arbitrary corruption processes across large state spaces. The forward process can be any continuous-time Markov chain. The reverse process only needs to match the marginal distributions at snapshot times, not reconstruct the full path between them.
The result: surpasses existing discrete diffusion methods in training efficiency and generation quality, competitive with autoregressive models on large-vocabulary tasks.
The structural principle: the full trajectory contains information the model doesn't need. Between any two snapshots, the exact corruption path is a nuisance variable — averaging over it gives the same generative quality with less computational cost. The shortcut is not an approximation. It's a recognition that the information content of the process lives at discrete checkpoints, not in the continuous path between them. The path is redundant; the snapshots are sufficient.