Timestep-free diffusion enables anytime solvers that scale beyond training depth

The key insight is that diffusion models don't actually need noise schedules to improve iteratively. By maintaining persistent hidden state across steps, the model can inject maximum noise at each inference pass and still converge, meaning you can add compute at test time without retraining or committing to a fixed depth upfront.

This connects directly to the latent refinement work from early September, which showed that frozen models can achieve deeper reasoning by iteratively refining continuous representations rather than expanding token sequences. Both papers solve the same underlying problem: how to decouple reasoning depth from model capacity. The diffusion paper adds a specific mechanism (noise injection without scheduling) that the latent refinement work didn't explore, suggesting multiple architectural paths exist to the same capability. The attention-diffusion equivalence paper from the same period also becomes relevant here, since if diffusion and attention are fundamentally solving the same problem, this timestep-free approach might generalize to transformer-based iterative solvers too.

If the same 99.90% Sudoku-Extreme accuracy holds when the model is forced to stop at shallow depths (say, 2-3 steps) during training but allowed to run 50+ steps at inference, that confirms the anytime solver claim. If accuracy degrades significantly at shallow training depths, the result may depend on implicit depth conditioning that the paper's framing obscures.