PaTh Adds Recursive Latent Reasoning to Diffusion Models, Solving 92.5% of Hard Sudokus at 10M Params
jwvdm · x · 2026-10-13
Researchers from Warsaw University of Technology and NYU published an arXiv paper, Think Before You Paint: Recursive Latent Reasoning for Diffusion Models, introducing Painter-Thinker (PaTh), which ports symbolic recursive reasoning (à la TRM) into pixel space.
Method: A small 10M-parameter recursive network (the Thinker) reasons over a grid of learned tokens encoding the noisy image and conditioning, refining a latent state within every denoising step, then steers a frozen diffusion model (the Painter) via ControlNet adapters. Training uses only reconstruction loss — no symbolic targets, solver, or verifier.
Results:
- Solves 92.5% of hard MNIST Sudokus (prior best 75%) and 71.2% of extreme ones (prior best 4.1%)
- Only 10M parameters vs 82M for a standard diffusion model
- Also improves mazes, Queens, and CLEVR spatial-relation tasks, with the gap widening as problems get harder (85% vs 62% at 10 CLEVR objects)
- Diagnostic experiments show PaTh recovers from injected mistakes that the base diffusion model cannot repair
The takeaway: reasoning mechanisms built for symbolic data can be integrated into pixel-space diffusion models, closing their gap on rule-governed visual reasoning tasks.
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