arXiv:2609.38364v1 Announce Type: cross Abstract: Discrete diffusion models and flow matching have emerged as powerful frameworks for generative modeling over discrete state spaces, yet efficient few...
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 introduces Finsler Flow Matching (FFM), a method for learning continuous stochastic dynamics from discrete Markov transition graphs in single‑cell snapshot data. FFM constructs a Finsler geometry using first and second local moments, learns directed geodesics via neural networks, and employs these to build geometry‑aware stochastic paths that can be simulated without explicit score or flow matching. Benchmark tests show that FFM better recovers intermediate cellular states, especially when dynamics are directional or anisotropic.
Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as $τ$-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied.
arXiv:2607. 15273v1 Announce Type: cross Abstract: MeanFlow generators achieve fast few-step sampling by predicting average velocities over time intervals, making them attractive for efficient generation.
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
arXiv:2606. 16073v1 Announce Type: new Abstract: Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling.
arXiv:2606. 24140v1 Announce Type: new Abstract: Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics.
arXiv:2607. 21427v1 Announce Type: new Abstract: Discrete flow matching provides a flexible framework for generative modeling on discrete structures.
The paper introduces dFlowGRPO, a reinforcement learning framework tailored for discrete flow models (DFMs). It generalizes previous work on diffusion large language models by supporting various probability paths and non-masked source distributions, and formulates denoising as a Markov decision process that leverages transition rates and posterior models. Experiments on the multimodal DFM FUDOKI show that dFlowGRPO outperforms existing GRPO methods on text‑to‑image generation and matches continuous flow models on multimodal understanding tasks.
arXiv:2605.05736v3 Announce Type: replace Abstract: Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. Ho...
arXiv:2603. 10718v3 Announce Type: replace Abstract: Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE.