We argue that in addition to training signals, enhancing the expressiveness of the policy class is crucial for the performance gains in RL. Flow-based generative models offer such potential, excelling at capturing complex, multimodal action distributions. However, their direct application in online RL is challenging due to a fundamental objective mismatch: standard flow training optimizes for static data imitation, while RL requires value-based policy optimization through a dynamic buffer, leading to difficult optimization landscapes.

Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models practically usable. However, certain synthesis process decisions still rely on heuristics without a solid theoretical foundation. In our work, we offer a novel analysis of the DM's inference process, introducing a comprehensive frequency response perspective. Specifically, by relying on Gaussianity assumption, we present the inference process as a closed-form spectral transfer function, capturing how the generated signal evolves in response to the initial noise. We demonstrate how the proposed analysis can be leveraged to design a noise schedule that aligns effectively with the characteristics of the data. The spectral perspective also provides insights into the underlying dynamics and sheds light on the relationship between spectral properties and noise schedule structure. Our results lead to scheduling curves that are dependent on the spectral content of the data, offering a theoretical justification for some of the heuristics taken by practitioners.

While successful, these methods are mainly designed for sampling from unconstrained domains.

Learning a stationary diffusion amounts to estimating the parameters of a stochastic differential equation whose stationary distribution matches a target distribution. We build on the recently introduced kernel deviation from stationarity (KDS), which enforces stationarity by evaluating expectations of the diffusion's generator in a reproducing kernel Hilbert space. Leveraging the connection between KDS and Stein discrepancies, we introduce the Stein-type KDS (SKDS) as an alternative formulation. We prove that a vanishing SKDS guarantees alignment of the learned diffusion's stationary distribution with the target. Furthermore, under broad parametrizations, SKDS is convex with an empirical version that is $ε$-quasiconvex with high probability. Empirically, learning with SKDS attains comparable accuracy to KDS while substantially reducing computational cost and yields improvements over the majority of competitive baselines.

EEG recordings contain rich information about neural activity but are subject to artifacts, noise, and superficial differences due to sensors, amplifiers, and filtering. Independent component analysis and automatic labeling of independent components (ICs) enable artifact removal in EEG pipelines. Convolutional Monge Mapping Normalization (CMMN) is a recent tool used to achieve spectral conformity of EEG signals, which was shown to improve deep neural network approaches for sleep staging. Here we propose a novel extension of the CMMN method with two alternative approaches to computing the source reference spectrum the target signals are mapped to: (1) channel-averaged and $l_1$-normalized barycenter, and (2) a subject-to-subject mapping that finds the source subject with the closest spectrum to the target subject. Notably, our extension yields space-time separable filters that can be used to map between datasets with different numbers of EEG channels. We apply these filters in an IC classification task, and show significant improvement in recognizing brain versus non-brain ICs. Clinical relevance - EEG recordings are used in the diagnosis and monitoring of multiple neuropathologies, including epilepsy and psychosis. While EEG analysis can benefit from automating artifact removal through independent component analysis and labeling, differences in recording equipment and context (the presence of noise from electrical wiring and other devices) may impact the performance of machine learning models, but these differences can be minimized by appropriate spectral normalization through filtering.

While successful, these methods are mainly designed for sampling from unconstrained domains.

We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for heavily restricted problem formulations -- or require expensive simulation to numerically obtain the time-dependent densities and sample from the diffusion process. In contrast, we propose a coupled parameterization which jointly models a time-dependent density function, or probability path, and the dynamics of a diffusion process that generates this probability path. To accomplish this, our approach directly bakes in the Fokker-Planck equation and density function requirements as hard constraints, by extending and greatly simplifying the construction of Neural Conservation Laws. This enables simulation-free training for a large variety of problem formulations, from data-driven objectives as in generative modeling and dynamical optimal transport, to optimality-based objectives as in stochastic optimal control, with straightforward extensions to mean-field objectives due to the ease of accessing exact density functions. We validate our method in a diverse range of application domains from modeling spatio-temporal events to learning optimal dynamics from population data.

We present \textbf{FlowRL}, a novel framework for online reinforcement learning that integrates flow-based policy representation with Wasserstein-2-regularized optimization. We argue that in addition to training signals, enhancing the expressiveness of the policy class is crucial for the performance gains in RL. Flow-based generative models offer such potential, excelling at capturing complex, multimodal action distributions. However, their direct application in online RL is challenging due to a fundamental objective mismatch: standard flow training optimizes for static data imitation, while RL requires value-based policy optimization through a dynamic buffer, leading to difficult optimization landscapes. FlowRL first models policies via a state-dependent velocity field, generating actions through deterministic ODE integration from noise. We derive a constrained policy search objective that jointly maximizes Q through the flow policy while bounding the Wasserstein-2 distance to a behavior-optimal policy implicitly derived from the replay buffer. This formulation effectively aligns the flow optimization with the RL objective, enabling efficient and value-aware policy learning despite the complexity of the policy class. Empirical evaluations on DMControl and Humanoidbench demonstrate that FlowRL achieves competitive performance in online reinforcement learning benchmarks.

We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards one density to the other. We call these information measures transport f-divergences. We present several properties of transport $f$-divergences, including invariances, convexities, variational formulations, and Taylor expansions in terms of mapping functions. Examples of transport f-divergences in generative models are provided.