The paper introduces the Latent Generative Solver (LGS), a neural PDE solver that combines a Physics VAE, a Pyramidal Flow-Forcing Transformer, and input noising to achieve generalization across twelve PDE families and stable long-term rollouts. LGS matches or surpasses deterministic baselines on one-step predictions, outperforms them on 5- and 10-step rollouts, and significantly reduces long-horizon error while cutting compute costs. It also adapts efficiently to unseen higher-resolution systems, demonstrating strong empirical performance on 2D regular-grid PDE simulations.
By Zituo Chen, Sili Deng
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
By Shiheng Zhang
arXiv:2607. 10203v2 Announce Type: replace-cross Abstract: Adaptive-compute world models -- early-exit or mixture-of-depths predictors that spend variable depth per step -- assume depth buys better predictions and can be routed adaptively.
By Achyuthan Sivasankar
arXiv:2608.23094v1 Announce Type: new
Abstract: One implicit DDIM inversion step is the cheapest probe of whether a pretrained diffusion model encodes local manifold geometry. It is the stationarity...
By Gordei Verbii
arXiv:2607. 10203v1 Announce Type: cross Abstract: Adaptive-compute world models -- early-exit or mixture-of-depths predictors that spend variable depth per step -- assume depth buys better predictions and can be routed adaptively.
By Achyuthan Sivasankar
Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories.