Original title: Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning
Mariia Drozdova, Aidan Sirbu, Pietro Miotti, Robert Obryk +3 · September 2026
Hard reasoning tasks usually require an AI to think step by step, but teaching models to keep improving with more time is difficult. Researchers connected two approaches: diffusion modelsAI models that generate data by gradually adding and then removing noise., which clean up noisy data in steps, and recursive solvers, which reuse their thoughts. They added a lasting memory to a diffusion model and removed its reliance on time steps, creating one rule that can run as long as needed. The model keeps getting more accurate the longer it runs. It reached a 99.90% exact solve rate on Sudoku-Extreme and a 98.93% solve rate on Maze-Unique. It can even solve puzzles by continuously injecting fresh random noise at each step, finding answers without extra tools or parallel guesses.
Imagine practicing a musical instrument by starting with simple scales and building up to complex pieces. After enough practice, you might find you can play a difficult piece directly without warming up with the scales. Here, the model trains with a structured schedule of noise addition and removal, but when solving puzzles, it can use constant noise and still work correctly.
For developers building AI that solves complex problems step-by-step, this means they can skip the gradual noise reduction that was thought necessary. The system works just as well with constant noise, cutting down on computational steps and making deployment simpler.
The abstract only demonstrates results on Sudoku and maze puzzles, so it's unclear if this method works for other types of reasoning tasks. Additionally, the training still depends on a specific corruption schedule, meaning the inference simplification doesn't apply to the learning phase.
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Diffusion as a Training Curriculum for Timestep-Free Iterative Reasoning — Mariia Drozdova, Aidan Sirbu, Pietro Miotti et al.
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.