Radar-based precipitation nowcasting, the task of forecasting short-term precipitation fields from previous radar images, is a critical problem for flood risk management and decision-making. While deep learning has substantially advanced this field, two challenges remain fundamental: the uncertainty of atmospheric dynamics and the efficient modeling of high-dimensional data. Diffusion models have shown strong promise by producing sharp, reliable forecasts, but their iterative sampling process is computationally prohibitive for time-critical applications. We introduce FlowCast, the first end-to-end probabilistic model leveraging Conditional Flow Matching (CFM) as a direct noise-to-data generative framework for precipitation nowcasting. Unlike hybrid approaches, FlowCast learns a direct noise-to-data mapping in a compressed latent space, enabling rapid, high-fidelity sample generation. Our experiments demonstrate that FlowCast establishes a new state-of-the-art in probabilistic performance while also exceeding deterministic baselines in predictive accuracy. A direct comparison further reveals the CFM objective is both more accurate and significantly more efficient than a diffusion objective on the same architecture, maintaining high performance with significantly fewer sampling steps. This work positions CFM as a powerful and practical alternative for high-dimensional spatiotemporal forecasting.

We present a comprehensive comparative study of three generative modeling paradigms: Denoising Diffusion Probabilistic Models (DDPM), Conditional Flow Matching (CFM), and MeanFlow. While DDPM and CFM require iterative sampling, MeanFlow enables direct one-step generation by modeling the average velocity over time intervals. We implement all three methods using a unified TinyUNet architecture (<1.5M parameters) on CIFAR-10, demonstrating that CFM achieves an FID of 24.15 with 50 steps, significantly outperforming DDPM (FID 402.98). MeanFlow achieves FID 29.15 with single-step sampling -- a 50X reduction in inference time. We further extend CFM to image inpainting, implementing mask-guided sampling with four mask types (center, random bbox, irregular, half). Our fine-tuned inpainting model achieves substantial improvements: PSNR increases from 4.95 to 8.57 dB on center masks (+73%), and SSIM improves from 0.289 to 0.418 (+45%), demonstrating the effectiveness of inpainting-aware training.

Subject-driven image generation aims to synthesize novel depictions of a specific subject across diverse contexts while preserving its core identity features. Achieving both strong identity consistency and high prompt diversity presents a fundamental trade-off. We propose a LoRA fine-tuned diffusion model employing a latent concatenation strategy, which jointly processes reference and target images, combined with a masked Conditional Flow Matching (CFM) objective. This approach enables robust identity preservation without architectural modifications. To facilitate large-scale training, we introduce a two-stage Distilled Data Curation Framework: the first stage leverages data restoration and VLM-based filtering to create a compact, high-quality seed dataset from diverse sources; the second stage utilizes these cu-rated examples for parameter-efficient fine-tuning, thus scaling the generation capability across various subjects and contexts. Finally, for filtering and quality assessment, we present CHARIS, a fine-grained evaluation framework that performs attribute-level comparisons along five key axes: identity consistency, prompt adherence, region-wise color fidelity, visual quality, and transformation diversity.

Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by slow sampling: producing a single sample requires solving a nonlinear ODE with hundreds of function evaluations. Recent approaches such as Rectified Flow and OT-CFM accelerate sampling by straightening trajectories, yet the learned dynamics remain nonlinear black boxes, limiting both efficiency and interpretability. We propose a fundamentally different perspective: globally linearizing flow dynamics via Koopman theory. By lifting Conditional Flow Matching (CFM) into a higher-dimensional Koopman space, we represent its evolution with a single linear operator. This yields two key benefits. First, sampling becomes one-step and parallelizable, computed in closed form via the matrix exponential. Second, the Koopman operator provides a spectral blueprint of generation, enabling novel interpretability through its eigenvalues and modes. We derive a practical, simulation-free training objective that enforces infinitesimal consistency with the teacher's dynamics and show that this alignment preserves fidelity along the full generative path, distinguishing our method from boundary-only distillation. Empirically, our approach achieves competitive sample quality with dramatic speedups, while uniquely enabling spectral analysis of generative flows.

Conventional time-series generation often ignores domain-specific physical constraints, limiting statistical and physical consistency. We propose a hierarchical framework that embeds the inherent hierarchy of physical laws-conservation, dynamics, boundary, and empirical relations-directly into deep generative models, introducing a new paradigm of physics-informed inductive bias. Our method combines Fourier Neural Operators (FNOs) for learning physical operators with Conditional Flow Matching (CFM) for probabilistic generation, integrated via time-dependent hierarchical constraints and FNO-guided corrections. Experiments on harmonic oscillators, human activity recognition, and lithium-ion battery degradation show 16.3% higher generation quality, 46% fewer physics violations, and 18.5% improved predictive accuracy over baselines.

Institute of Materials Chemistry, TU Wien, A-1060 Vienna, Austria Conditional Flow Matching(CFM) represents a fast and high-quality approach to generative modelling, but in many applications it is of interest to steer the generated samples towards precise requirements. While steering approaches like gradient-based guidance, sequential Monte Carlo steering or Feynman-Kac steering are well established for diffusion models, they have not been extended to flow matching approaches yet. In this work, we formulate this requirement as tilting the output with an energy potential. We derive, for the first time, Feynman-Kac steering for CFM. We evaluate our approach on a set of synthetic tasks, including the generation of tilted distributions in a high-dimensional space, which is a particularly challenging case for steering approaches. We then demonstrate the impact of Feynman-Kac steered CFM on the previously unsolved challenge of generated transition states of chemical reactions with the correct chirality, where the reactants or products can have a different handedness, leading to geometric constraints of the viable reaction pathways connecting reactants and products. Code to reproduce this study is avaiable open-source at https://github.com/heid-lab/fkflow. I. INTRODUCTION Since its introduction by Lipman et al. [1], Conditional Flow Matching (CFM) has seen several interesting applications, ranging from image [1], audio [2] and video [3] generation to decision-making [4], time series modelling [5], protein modelling [6, 7] or molecular structure design [8], amongst others. CFM transforms samples from a source distribution (such as random noise) to samples following a given target distribution (such as images or molecular structures) by modelling probability paths via vector fields. It largely improves on diffusion-based methods both in quality and speed, establishing CFM as a popular generative method [1].

Current flow-based generative speech enhancement methods learn curved probability paths which model a mapping between clean and noisy speech. Despite impressive performance, the implications of curved probability paths are unknown. Methods such as Schrodinger bridges focus on curved paths, where time-dependent gradients and variance do not promote straight paths. Findings in machine learning research suggest that straight paths, such as conditional flow matching, are easier to train and offer better generalisation. In this paper we quantify the effect of path straightness on speech enhancement quality. We report experiments with the Schrodinger bridge, where we show that certain configurations lead to straighter paths. Conversely, we propose independent conditional flow-matching for speech enhancement, which models straight paths between noisy and clean speech. We demonstrate empirically that a time-independent variance has a greater effect on sample quality than the gradient. Although conditional flow matching improves several speech quality metrics, it requires multiple inference steps. We rectify this with a one-step solution by inferring the trained flow-based model as if it was directly predictive. Our work suggests that straighter time-independent probability paths improve generative speech enhancement over curved time-dependent paths.

Dysarthria is a neurological disorder that significantly impairs speech intelligibility, often rendering affected individuals unable to communicate effectively. This necessitates the development of robust dysarthric-to-regular speech conversion techniques. In this work, we investigate the utility and limitations of self-supervised learning (SSL) features and their quantized representations as an alternative to mel-spectrograms for speech generation. Additionally, we explore methods to mitigate speaker variability by generating clean speech in a single-speaker voice using features extracted from WavLM. To this end, we propose a fully non-autoregressive approach that leverages Conditional Flow Matching (CFM) with Diffusion Transformers to learn a direct mapping from dysarthric to clean speech. Our findings highlight the effectiveness of discrete acoustic units in improving intelligibility while achieving faster convergence compared to traditional mel-spectrogram-based approaches.

Achieving high-fidelity and temporally smooth 3D human motion generation remains a challenge, particularly within resource-constrained environments. We introduce FlowMotion, a novel method leveraging Conditional Flow Matching (CFM). FlowMotion incorporates a training objective within CFM that focuses on more accurately predicting target motion in 3D human motion generation, resulting in enhanced generation fidelity and temporal smoothness while maintaining the fast synthesis times characteristic of flow-matching-based methods. FlowMotion achieves state-of-the-art jitter performance, achieving the best jitter in the KIT dataset and the second-best jitter in the HumanML3D dataset, and a competitive FID value in both datasets. This combination provides robust and natural motion sequences, off ering a promising equilibrium between generation quality and temporal naturalness. Introduction The synthesis of 3D human body motion has diverse applications across fields such as robotics [1, 2, 3], VR/ AR [4, 5], entertainment [6, 7, 8, 9], and social interaction in virtual 3D spaces [10, 11, 12, 13]. While recent advances in 3D human motion generation are significant, several challenges remain. The inherent complexities of motion generation are exacerbated by the need to incorporate diverse constraints, such as spatial trajectories [14, 15], interactions with surrounding objects [16, 17], or temporal specifications defined by keyframes [18], all aimed at producing lifelike movements. To achieve realistic and context-aware motion synthesis, motion generation techniques frequently leverage data-driven motion capture data. Recent studies in generative models have driven the development of new techniques for synthesizing 3D human body motion. These methods primarily focus on generating realistic movements based on user inputs, especially descriptive text that specifies the intended action. A key advantage of these generative approaches is their ability to produce a diverse range of plausible motion sequences from a single prompt. This allows users to explore multiple interpretations of a desired movement and select the sequence that best aligns with their creative vision.

Integrating audio comprehension and generation into large language models (LLMs) remains challenging due to the continuous nature of audio and the resulting high sampling rates. Here, we introduce a novel approach that combines Variational Quantization with Conditional Flow Matching to convert audio into ultra-low bitrate discrete tokens of 0.23kpbs, allowing for seamless integration with text tokens in LLMs. We fine-tuned a pretrained text-based LLM using Low-Rank Adaptation (LoRA) to assess its effectiveness in achieving true multimodal capabilities, i.e., audio comprehension and generation. Our tokenizer outperforms a traditional VQ-VAE across various datasets with diverse acoustic events. Despite the substantial loss of fine-grained details through audio tokenization, our multimodal LLM trained with discrete tokens achieves competitive results in audio comprehension with state-of-the-art methods, though audio generation is poor. Our results highlight the need for larger, more diverse datasets and improved evaluation metrics to advance multimodal LLM performance.