Conditional Flow Matching

We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution. Hierarchical flow matching models the full conditional velocity law in velocity space, but its inner flow is asked to transport isotropic Gaussian noise to a multimodal target velocity distribution from scratch. Our key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target. CCVFM first compresses the target into weighted atoms using an entropic Sinkhorn coreset and lifts them to a Gaussian mixture. The induced conditional velocity law is then a closed-form Gaussian mixture that can be sampled without a learned neural sampler. A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual rather than learning an entire noise-to-data map. We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance. Empirically, on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ, the proposed method reaches competitive few-step generation under matched architectures.

Unlike standard expected-return Reinforcement Learning (RL), Distributional RL (DRL) models the full return distribution, making it better-suited for uncertainty-aware and risk-sensitive decision-making. Conditional Flow Matching (CFM) critics have recently attracted attention for modelling continuous, multi-modal return distributions. Despite this interest, there remains a substantial metric mismatch: DRL theory relies on the distributional Bellman operator being contractive in the $p$-Wasserstein distance, yet existing CFM critics are trained with arbitrary source-target couplings, so their flow-matching losses are not Wasserstein-aligned surrogates for matching Bellman target return distributions. In this work, we address this mismatch by proposing FlowIQN, a CFM critic that sorts source and Bellman target samples within each mini-batch to approximate the monotone optimal transport coupling, replacing arbitrary pairings with quantile-aligned flow paths. We prove that the loss of our quantile-coupled CFM critic yields a Wasserstein-aligned approximate projection compatible with the foundations of DRL. To our knowledge, FlowIQN is the first flow-matching distributional critic with an explicit Wasserstein-aligned projection guarantee. We further extend FlowIQN with shortcut models for efficient inference. Empirical results show that FlowIQN improves Wasserstein return-distribution accuracy over other CFM critics. It also yields competitive performance on offline RL benchmarks across multiple policy extraction methods, providing a theoretically grounded CFM critic that is readily compatible with DRL pipelines. Code: https://github.com/ori-goals/flowIQN.

We introduce a new generative modeling framework, \textbf{Flow Matching with Arbitrary Auxiliary Paths (AuxPath-FM)}, which generalizes conditional flow matching by incorporating an auxiliary variable drawn from an arbitrary distribution into the probability path. Unlike prior methods that restrict auxiliary components to Gaussian noise, AuxPath-FM allows the variable $η$ to follow any distribution, producing trajectories of the form $X_t = a(t)X_1 + b(t)X_0 + c(t)η$. We theoretically demonstrate that this construction preserves the continuity equation and maintains a training objective consistent with the marginal formulation. This flexibility enables the design of diverse probability paths using various priors, including Gaussian, Uniform, Laplace, and discrete Rademacher distributions, each offering unique geometric properties for generative flows. Furthermore, our framework allows for specialized tasks such as label-guided generation by encoding structured semantic information into the auxiliary distribution. Overall, AuxPath-FM provides a principled and general foundation for probability path design, offering both theoretical generality and practical flexibility for diverse generative modeling tasks.

In this study, deep learning is used to estimate kinetic parameters for modeling itaconic acid production based on real batch experiments conducted at different agitation speeds and reactor scales. Two deep learning strategies, namely direct deep learning (DDL) and generative conditional flow matching (CFM) are compared and benchmarked against nonlinear regression as a reference method. Compared with DDL, CFM consistently yields more accurate results. The concentration profiles predicted by CFM closely match those obtained from nonlinear regression, whereas DDL results in larger deviations. Similar behavior is observed in the scale-up experiments, where the CFM model again generalizes better and is more robust than the direct approach. These findings demonstrate that CFM can reliably predict system behavior across different operating conditions and scales, offering a flexible and data-efficient framework for parameter estimation in dynamic bioprocess models.

High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation. While Conditional Flow Matching (CFM) offers a robust acceleration approach, we demonstrate its standard training loss is fundamentally misleading. Specifically, utilizing a Jefferson Lab Nuclear Physics (NP) kinematic dataset ($γp \to ρ^0 p \to π^+π^- p$), we expose that CFM loss plateaus prematurely, obscuring ongoing physical refinement. To verify this disconnect is a dataset-agnostic pathology, we introduce ScatterPrism, an efficient generative surrogate evaluated against both the NP data and synthetic stress tests modeling challenging 1D distribution topologies. Coupling these benchmarks, we establish that physics-informed metrics continue improving long after standard loss converges. Consequently, we propose a multi-metric diagnostic protocol to ensure true kinematic fidelity without data memorization. Driven by NP challenges relevant to the forthcoming Electron-Ion Collider (EIC), this unified machinery has strong potential to extend to High-Energy Physics (HEP) applications, such as jet modeling. Furthermore, the framework holds promise for broader domains requiring rigorous generative reliability, including medical imaging, astrophysics, and quantitative finance.

Visually-guided acoustic highlighting seeks to rebalance audio in alignment with the accompanying video, creating a coherent audio-visual experience. While visual saliency and enhancement have been widely studied, acoustic highlighting remains underexplored, often leading to misalignment between visual and auditory focus. Existing approaches use discriminative models, which struggle with the inherent ambiguity in audio remixing, where no natural one-to-one mapping exists between poorly-balanced and well-balanced audio mixes. To address this limitation, we reframe this task as a generative problem and introduce a Conditional Flow Matching (CFM) framework. A key challenge in iterative flow-based generation is that early prediction errors -- in selecting the correct source to enhance -- compound over steps and push trajectories off-manifold. To address this, we introduce a rollout loss that penalizes drift at the final step, encouraging self-correcting trajectories and stabilizing long-range flow integration. We further propose a conditioning module that fuses audio and visual cues before vector field regression, enabling explicit cross-modal source selection. Extensive quantitative and qualitative evaluations show that our method consistently surpasses the previous state-of-the-art discriminative approach, establishing that visually-guided audio remixing is best addressed through generative modeling.