The paper introduces a density‑level backward‑error framework for low‑NFE generative ODE sampling, identifying the part of a solver’s modified‑equation defect that alters the evolving marginal while ignoring solenoidal trajectory distortion. This leads to a solver‑order‑aware compute‑allocation rule and an objective for choosing numerically favorable velocity representatives, distinct from schedule search or higher‑order solver design. Experiments on Gaussian, mixture models, and a pretrained CIFAR‑10 EDM probability‑flow ODE show that density‑aware allocation consistently improves fixed‑update Euler sampling in the low‑NFE regime and accelerates convergence to a dense Euler reference.
arXiv:2602.12624v2 Announce Type: replace Abstract: Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by h...
arXiv:2607. 14652v1 Announce Type: new Abstract: Topology optimisation (TO) often requires repeated finite element analysis and sensitivity-based material updates, which can be costly when multiple candidate designs are needed under varying physical and design conditions.
arXiv:2111. 10722v4 Announce Type: replace-cross Abstract: We propose a novel deterministic sampling method, EVI-MMD, to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD).
The paper introduces the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator that predicts divergence‑free velocity fields for incompressible density transport. VIOT combines a stream‑function representation, a regularized transport objective, and a Fourier Neural Operator backbone to amortize the solve across new source‑target pairs and grid resolutions. Experiments on 2D and 3D benchmarks show that VIOT produces full transport trajectories in seconds, achieving roughly a $10^4 imes$ speedup over per‑instance baselines that require hours of optimization.
arXiv:2608. 07042v1 Announce Type: cross Abstract: Rectified flows, also called flow matching or stochastic interpolants, are generative models that learn a time-dependent vector field steering a probability curve between two probability distributions, usually referred to as latent and target distributions.
The paper introduces Flow Divergence Sampler (FDS), a training‑free method that refines intermediate states in flow‑matching models by using the divergence of the marginal velocity field to detect and correct misguidance toward low‑density regions. FDS operates during inference, requires no additional training, and can be applied as a plug‑and‑play module with standard solvers and existing flow backbones. Experiments show that FDS consistently improves fidelity in tasks such as text‑to‑image synthesis and inverse problems.
arXiv:2606. 30376v1 Announce Type: new Abstract: Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods.
arXiv:2611.05605v1 Announce Type: new Abstract: Variational approaches to learning transport maps for multimodal sampling can suffer from mode collapse. One way to mitigate this problem is to learn t...
arXiv:2601.20250v2 Announce Type: replace Abstract: Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models,...
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.