Wave Function Collapse Meets Diffusion and Flow Matching

Wave function collapse (WFC) generates discrete layouts through compatibility rules and constraint propagation, while diffusion models and flow matching learn rich distributions over continuous outputs. We combine these complementary mechanisms for coarse-to-detailed scene generation: WFC-based layouts provide structural templates, while learned generative models refine their geometry and appearance. We consider two refinement mechanisms: structure-conditioned diffusion, which denoises from Gaussian noise, and WFC-source flow matching, which transports noisy template encodings towards detailed realisations. On 64 held-out procedural landscapes, both methods improve reconstruction over unrefined WFC templates, reducing MSE by 41.0% and 56.6%, respectively, with flow matching also achieving higher SSIM. We further formulate conditional Metropolis-Hastings correction and refinement-guided WFC as methodological extensions.