We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the effectiveness of our method on the discrete generation problem by instantiat-ing SFM on the manifold of categorical distributions whose geometric properties remain unexplored in previous discrete generative models. Utilizing the Fisher information metric, we equip the manifold with a Riemannian structure whose intrinsic geometries are effectively leveraged by following the shortest paths of geodesics. We develop an efficient training and sampling algorithm that overcomes numerical stability issues with a diffeomorphism between manifolds. Our distinctive geometric perspective of statistical manifolds allows us to apply optimal transport during training and interpret SFM as following the steepest direction of the natural gradient. Unlike previous models that rely on variational bounds for likelihood estimation, SFM enjoys the exact likelihood calculation for arbitrary probability measures. We manifest that SFM can learn more complex patterns on the statistical manifold where existing models often fail due to strong prior assumptions. Comprehensive experiments on real-world generative tasks ranging from image, text to biological domains further demonstrate that SFM achieves higher sampling quality and likelihood than other discrete diffusion or flow-based models. Our code is available at https://github.com/ccr-cheng/

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the effectiveness of our method on the discrete generation problem by instantiating SFM on the manifold of categorical distributions whose geometric properties remain unexplored in previous discrete generative models. Utilizing the Fisher information metric, we equip the manifold with a Riemannian structure whose intrinsic geometries are effectively leveraged by following the shortest paths of geodesics. We develop an efficient training and sampling algorithm that overcomes numerical stability issues with a diffeomorphism between manifolds. Our distinctive geometric perspective of statistical manifolds allows us to apply optimal transport during training and interpret SFM as following the steepest direction of the natural gradient. Unlike previous models that rely on variational bounds for likelihood estimation, SFM enjoys the exact likelihood calculation for arbitrary probability measures. We manifest that SFM can learn more complex patterns on the statistical manifold where existing models often fail due to strong prior assumptions. Comprehensive experiments on real-world generative tasks ranging from image, text to biological domains further demonstrate that SFM achieves higher sampling quality and likelihood than other discrete diffusion or flow-based models.

Vision-language-action (VLA) models have recently emerged as a powerful paradigm for building generalist robots. However, traditional VLA models that generate actions through flow matching (FM) typically rely on rigid and uniform time schedules, i.e., synchronous FM (SFM). Without action context awareness and asynchronous self-correction, SFM becomes unstable in long-horizon tasks, where a single action error can cascade into failure. In this work, we propose asynchronous flow matching VLA (AsyncVLA), a novel framework that introduces temporal flexibility in asynchronous FM (AFM) and enables self-correction in action generation. AsyncVLA breaks from the vanilla SFM in VLA models by generating the action tokens in a non-uniform time schedule with action context awareness. Besides, our method introduces the confidence rater to extract confidence of the initially generated actions, enabling the model to selectively refine inaccurate action tokens before execution. Moreover, we propose a unified training procedure for SFM and AFM that endows a single model with both modes, improving KV-cache utilization. Extensive experiments on robotic manipulation benchmarks demonstrate that AsyncVLA is data-efficient and exhibits self-correction ability. AsyncVLA achieves state-of-the-art results across general embodied evaluations due to its asynchronous generation in AFM. Our code is available at https://github.com/YuhuaJiang2002/AsyncVLA.

Intra - sentence multilingual speech synthesis (code - switching TTS) remains a major challenge due to abrupt language shifts, varied scripts, and mismatched prosody between languages. Conventional TTS systems are typically monolingual and fail to produce natural, intelligible speech in mixed - language contexts. We introduce Script - First Multilingual Synthesis with Adaptive Locale Resolution (SFMS - ALR) an engine - agnostic framework for fluent, real - time code - switched speech generation. SFMS - ALR segments input text by Unicode script, applies adaptive language identification to determine each segment's language and locale, and normalizes prosody using sentiment - aware adjustments to preserve expressive continuity across languages. The algorithm generates a unified SSML representation with appropriate or spans and synthesizes the utterance in a single TTS request. Unlike end - to - end multilingual models, SFMS - ALR requires no retraining and integrates seamlessly with existing voices from Google, Apple, Amazon, and other providers. Comparative analysis with data - driven pipelines such as Unicom and Mask LID demonstrates SFMS - ALR's flexibility, interpretability, and immediate deployability . The framework establishes a modular baseline for high - quality, engine - independent multilingual TTS and outlines evaluation strategies for intelligibility, naturalness, and user preference.

We propose Shallow Flow Matching (SFM), a novel mechanism that enhances flow matching (FM)-based text-to-speech (TTS) models within a coarse-to-fine generation paradigm. Unlike conventional FM modules, which use the coarse representations from the weak generator as conditions, SFM constructs intermediate states along the FM paths from these representations. During training, we introduce an orthogonal projection method to adaptively determine the temporal position of these states, and apply a principled construction strategy based on a single-segment piecewise flow. The SFM inference starts from the intermediate state rather than pure noise, thereby focusing computation on the latter stages of the FM paths. We integrate SFM into multiple TTS models with a lightweight SFM head. Experiments demonstrate that SFM yields consistent gains in speech naturalness across both objective and subjective evaluations, and significantly accelerates inference when using adaptive-step ODE solvers. Demo and codes are available at https://ydqmkkx.github.io/SFMDemo/.

Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional data is often hindered by challenges such as privacy constraints, sparse and irregular sampling, infinite dimensionality, and non-Gaussian structures. To address these challenges, we introduce a novel framework named Smooth Flow Matching (SFM), tailored for generative modeling of functional data to enable statistical analysis without exposing sensitive real data. Built upon flow-matching ideas, SFM constructs a semiparametric copula flow to generate infinite-dimensional functional data, free from Gaussianity or low-rank assumptions. It is computationally efficient, handles irregular observations, and guarantees the smoothness of the generated functions, offering a practical and flexible solution in scenarios where existing deep generative methods are not applicable. Through extensive simulation studies, we demonstrate the advantages of SFM in terms of both synthetic data quality and computational efficiency. We then apply SFM to generate clinical trajectory data from the MIMIC-IV patient electronic health records (EHR) longitudinal database. Our analysis showcases the ability of SFM to produce high-quality surrogate data for downstream statistical tasks, highlighting its potential to boost the utility of EHR data for clinical applications.

The SENCOTEN language, spoken on the Saanich peninsula of southern Vancouver Island, is in the midst of vigorous language revitalization efforts to turn the tide of language loss as a result of colonial language policies. To support these on-the-ground efforts, the community is turning to digital technology. Automatic Speech Recognition (ASR) technology holds great promise for accelerating language documentation and the creation of educational resources. However, developing ASR systems for SENCOTEN is challenging due to limited data and significant vocabulary variation from its polysynthetic structure and stress-driven metathesis. To address these challenges, we propose an ASR-driven documentation pipeline that leverages augmented speech data from a text-to-speech (TTS) system and cross-lingual transfer learning with Speech Foundation Models (SFMs). An n-gram language model is also incorporated via shallow fusion or n-best restoring to maximize the use of available data. Experiments on the SENCOTEN dataset show a word error rate (WER) of 19.34% and a character error rate (CER) of 5.09% on the test set with a 57.02% out-of-vocabulary (OOV) rate. After filtering minor cedilla-related errors, WER improves to 14.32% (26.48% on unseen words) and CER to 3.45%, demonstrating the potential of our ASR-driven pipeline to support SENCOTEN language documentation.