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Spatial Reasoning with Denoising Models
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Introduces Spatial Reasoning Models, denoising generative models that sample per-patch noise levels so that spatial variables can be generated in a chosen sequential order, reducing hallucination on reasoning benchmarks such as MNIST Sudoku.
Problem
Diffusion and flow-matching models hallucinate when generating spatially complex, multi-variable distributions, failing at reasoning tasks that require consistent conditional generation across image patches.
Approach
Train a single denoiser with individual per-patch noise levels (sampled via a uniform-mean scheme with recursive allocation) so that sampling can interpolate between parallel diffusion and autoregressive generation, and use the network's own predicted uncertainty to pick a greedy generation order.
Key results
- On MNIST Sudoku hard, predicted-order sampling without overlap reaches 51.6% accuracy versus 0.8% for the parallel diffusion baseline, using the same trained model.
- On Even Pixels, SRM with predicted order + overlap reaches 0.518 accuracy versus 0.250 for the diffusion model.
- On Counting Polygons/Stars FFHQ (stars), predicted order + overlap reaches 0.150 accuracy versus 0.070 for the diffusion model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use predicted uncertainty order without overlap instead of parallel denoising | SRM · MNIST Sudoku hard | accuracy: 0.010 -> 0.516 | Helped |
| Use predicted uncertainty order rather than random order, without overlap | SRM · MNIST Sudoku hard | accuracy: 0.024 -> 0.516 | Helped |
| Use predicted uncertainty order rather than graph-based order, without overlap | SRM · MNIST Sudoku hard | accuracy: 0.266 -> 0.516 | Helped |
| Add overlap between successive denoising intervals | SRM with predicted order · MNIST Sudoku hard | accuracy: 0.516 -> 0.422 | Hurt |
| Use predicted order rather than random order with overlap | SRM · Even Pixels | accuracy: 0.476 -> 0.518 | Helped |
| Add overlap to sequential sampling | SRM · Even Pixels | accuracy | Helped |
| Use sequential sampling rather than parallel generation | SRM · Counting Stars FFHQ | accuracy: 0.034 -> 0.150 | Helped |
| Use sequential sampling rather than parallel generation | SRM · Counting Stars FFHQ | consistency: 0.576 -> 0.888 | Helped |
| Use Uniform mean noise-level sampling rather than independent Uniform t sampling (ablation) | SRM with predicted order without overlap · MNIST Sudoku hard | accuracy: 0.018 -> 0.516 | Helped |
| Use stochastic rather than deterministic sampling (ablation) | SRM with predicted order without overlap · MNIST Sudoku hard | accuracy: 0.500 -> 0.516 | Helped |
| Lower noise-level sampling sharpness from 0.75 to 0.50 (ablation) | SRM with predicted order and overlap · Even Pixels | accuracy: 0.518 -> 0.368 | Hurt |
| Raise noise-level sampling sharpness from 0.75 to 1.00 (ablation) | SRM with predicted order and overlap · Even Pixels | accuracy: 0.518 -> 0.484 | Hurt |
Surprising findings
- Parallel sampling of the SRM performs similarly to the standard diffusion baseline on Sudoku, indicating parallel denoising is inappropriate for complex dependencies regardless of training.
- Uncertainty predicted by the denoising network itself gives a generation order that outperforms a manually defined dependency-graph order on Sudoku.
Limitations
- Models remain far from optimally solving the benchmark tasks; Counting Polygons/Stars accuracy stays low (under 20%).
- Graph-based order ignores weak versus strong conditioning and relies only on noise levels for certainty.
- Experiments are limited to small synthetic benchmarks with lightweight UNets and DiT in pixel space.
Experimental setup
Datasets: MNIST FFHQ MNIST Sudoku (constructed) Even Pixels (constructed) Counting Polygons/Stars FFHQ (constructed)
Benchmarks: MNIST Sudoku Even Pixels Counting Polygons/Stars FFHQ
Metrics: accuracy L1 error consistency
Baselines: Diffusion Model (inpainting) Diffusion Forcing sampling Random Order Graph-based Order Oracle solver
Builds on: Diffusion Forcing DDPM DDIM rectified flow MAR
Closest papers by meaning
- SpatialLadder: Progressive Training for Spatial Reasoning in Vision-Language Models (ICLR 2026 · similarity 0.88)
- SpatiaLab: Can Vision–Language Models Perform Spatial Reasoning in the Wild? (ICLR 2026 · similarity 0.87)
- Advancing Spatial Reasoning in Large Language Models: An In-Depth Evaluation and Enhancement Using the StepGame Benchmark (AAAI 2024 · similarity 0.87)
- SpatialRGPT: Grounded Spatial Reasoning in Vision-Language Models (NeurIPS 2024 · similarity 0.87)
- Spatial-DISE: A Unified Benchmark for Evaluating Spatial Reasoning in Vision-Language Models (ICLR 2026 · similarity 0.87)
- Is A Picture Worth A Thousand Words? Delving Into Spatial Reasoning for Vision Language Models (NeurIPS 2024 · similarity 0.87)
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