The paper proposes a new approach to likelihood approximation for complex simulation models using a chain of aggregated normalizing flows. It describes a sequential estimation strategy where each set of bijective transformations is optimized independently, enabling scalable and controllable simulation routines for large‑scale data analysis. The framework also offers a surrogate model that facilitates sample generation, Bayesian inference, hypothesis testing, and uncertainty quantification.
By Getachew K Befekadu
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.
By Weiguo Gao, Ming Li, Lei Shi, Hanfei Zhou
Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching. Along the way, the underlying techniques have become more complicated and various beliefs about what drives strong empirical performance have taken hold.
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.
By Ishan Nath, Tom Stanic, Avishek Joey Bose, Gauthier Gidel, Quentin Bertrand
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.
By Lei Luo, Yingzhen Zhang, Jian Yang
The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
By Yixuan Sun, Anirban Samaddar, Sandeep Madireddy
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
By Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang
arXiv:2607. 19332v1 Announce Type: new Abstract: Generative models have undergone many generations of evolution, from VAEs/GANs to diffusion/flow matching.
By Chirag Vashist, Ke Li
arXiv:2605.06140v3 Announce Type: replace-cross
Abstract: Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such...
By Samir Darouich, Vinh Tong, Llu\'is Pastor-P\'erez, Tanja Bien, Loay Mualem, Mathias Niepert
arXiv:2606. 08802v1 Announce Type: new Abstract: Standard flow and diffusion pre-training matches the distribution of available data (e.
By Riccardo De Santi, Bruce Lee, Cristian Perez Jensen, Kimon Protopapas, Sophia Tang, Cheng-Hao Liu, Pranam Chatterjee, Yisong Yue, Andreas Krause
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
By Fanghui Song, Zhongjian Wang, Jiebao Sun
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan