Physics-Constrained Generative World Model for Off-Road Terrain via Post-hoc Projection

Generative models for physically grounded terrain face a persistent tradeoff: training-time physics losses distort the learned distribution, while unconstrained generators routinely produce physically impossible surfaces. We \emph{decouple} generation quality from constraint satisfaction entirely, enforcing slope stability, bearing capacity, and surface continuity via a closed-form \emph{post-hoc projection} applied to the generator's output. The projection raises the physics pass rate from $53\%$ to $\mathbf{100\%}$ on a diffusion generator with no change in FID ($13.72$), whereas a matched PhysLoss baseline degrades FID to $56.6$ ---a $4{\times}$ loss of generation quality---while reaching only $25.5\%$ pass rate. The projection is \emph{model-agnostic}: on four diverse generators (Procedural, Diffusion, VAE, GAN) it consistently yields $89.5\%$--$100\%$ compliance with $<4.3\%$ overhead. Out-of-distribution evaluation on real TartanDrive terrain confirms transfer: all four generators reach $100\%$ pass rate, while projection simultaneously improves BEV-FID against the real reference by up to $20\%$. We instantiate the layer inside DreamEnv, an end-to-end BEV world model.