The paper introduces methods to improve training of stochastic flow maps for stochastic differential equations. It proposes representing Brownian paths with a shifted Legendre polynomial basis and using a Wong‑Zakai styled objective to enable derivative‑based losses. The authors also provide a fine‑tuning recipe that turns large pre‑trained flow models into strong stochastic flow maps, achieving a three‑fold improvement on ImageNet compared to SSFM.
arXiv:2606. 01086v1 Announce Type: cross Abstract: Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation.
arXiv:2607. 26398v1 Announce Type: new Abstract: Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.
arXiv:2606. 11156v1 Announce Type: cross Abstract: Recent one-step generative models accelerate sampling by learning deterministic flow maps of the underlying dynamics.
arXiv:2607. 00535v1 Announce Type: cross Abstract: Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning long-range transport maps between noise and data.
The paper investigates the training dynamics of flow map models, which convert diffusion trajectories into one‑step samplers for efficient probabilistic generation. It provides a theoretical analysis of the functional gradient flow induced by MeanFlow and Lagrangian losses, proving their convergence to the true flow map and identifying the risk of unbounded updates. The authors show that adaptive normalization and a specific reweighting scheme not only bound updates but also guarantee convergence to a neighborhood of the solution, and they confirm these findings with synthetic experiments and image‑generation benchmarks.
arXiv:2606. 06272v1 Announce Type: new Abstract: Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph.
arXiv:2610.01408v1 Announce Type: new Abstract: Trajectory crossing remains a critical bottleneck in Flow Matching (FM), and previous works typically view these crossings from a theoretical optimizat...
We study path-flow alignment as a unified training objective for flow matching. Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving p...
arXiv:2606. 14283v1 Announce Type: cross Abstract: Deep learning has driven many recent advances in process analytics, especially for predictive and prescriptive monitoring.
The book "The Principles of Diffusion Models" outlines the foundational concepts behind diffusion models, tracing their evolution from a forward process that corrupts data into noise to a reverse process that reconstructs data. It presents three complementary perspectives—variational, score-based, and flow-based—each describing how a time-dependent velocity field transports a simple prior to the data distribution. The text also covers practical guidance for controllable generation, efficient solvers, and diffusion-inspired flow-map models, providing a mathematically grounded framework for readers with basic deep‑learning knowledge.
The paper presents an amortized neural sampler that merges operator learning with flow-based methods to efficiently sample from invariant measures of stochastic differential equations (SDEs). By mapping SDE coefficient functions to pushforwards from a reference measure, the approach shifts the sampling cost to an initial training phase, after which new SDE instances can be sampled with a single encoder pass and a few ODE solver steps, independent of mixing time. The framework incorporates Lagrangian trajectory sensors and cross attention to handle high-dimensional problems, and the authors provide theoretical guarantees of expressivity and resolution invariance, demonstrating competitive accuracy and significant speedups over MCMC in 1D, 2D, and 64D SDE families.
The paper introduces Diffusion-Enhanced GFlowNet (DEG), a framework that combines Generative Flow Networks with diffusion models to improve vehicle routing problem solutions. DEG uses GFlowNet to generate edge-level signals, perturbs them with diffusion noise, and denoises them to expand flow into high-reward regions, thereby increasing solution diversity. A scalable decoder is added, and experiments on synthetic and real datasets—including up to 10,000-node instances—show DEG outperforms baseline methods.