DPMs, those inherent factors can be automatically discovered, explicitly represented, and clearly injected into the diffusion process via the sub-gradient fields. To tackle this task, we devise an unsupervised approach named DisDiff, achieving disentangled representation learning in the framework of DPMs.

The contributions of this paper are as follows (Figure 1): 1.

We prove that if these charges flow upward along electric field lines, their initial distribution in the z = 0 plane transforms into a distribution on the hemisphere of radiusr that becomes uniform in the r limit. To learn the bijective transformation, we estimate the normalized field in the augmented space.

The aim of this work is to learn models of population dynamics of physical systems that feature stochastic and mean-field effects and that depend on physics parameters. The learned models can act as surrogates of classical numerical models to efficiently predict the system behavior over the physics parameters. Building on the Benamou-Brenier formula from optimal transport and action matching, we use a variational problem to infer parameter-and time-dependent gradient fields that represent approximations of the population dynamics. The inferred gradient fields can then be used to rapidly generate sample trajectories that mimic the dynamics of the physical system on a population level over varying physics parameters. We show that combining Monte Carlo sampling with higher-order quadrature rules is critical for accurately estimating the training objective from sample data and for stabilizing the training process. We demonstrate on Vlasov-Poisson instabilities as well as on high-dimensional particle and chaotic systems that our approach accurately predicts population dynamics over a wide range of parameters and outperforms state-of-the-art diffusion-based and flow-based modeling that simply condition on time and physics parameters.

The main goal of generative modeling is to use finitely many samples from a distribution to construct a sampling scheme capable of generating new samples from the same distribution. Among the families of existing generative models, flow matching (FM) [23, 24] is notable for its flexibility and simplicity. Given a target probability distribution, FM utilizes a parametric model (e.g., neural network) to learn the velocity vector field that defines a deterministic, continuous transformation (a normalizing flow) and transports a source probability distribution (e.g., standard Gaussian) to the target distribution. While the population formulation of FM often exhibits appealing structure--sometimes even admitting gradient-field velocities--practical models are trained on finite datasets and therefore optimize empirical objectives. This empirical setting substantially alters the geometry of the learned velocity field and the energetic properties of the resulting sampler. These notes aim to clarify how empirical FM behaves, how it differs from its population counterpart, and what implicit biases arise in the learned sampling dynamics. From now on, we assume that all the probability distributions/measures (except the empirical distribution) of the random variables considered are absolutely continuous (i.e., they have densities with respect to the Lebesgue measure), in which case we shall abuse the notation and use the same symbol to denote both the distribution and the density. To maintain the flow of the main text, we defer discussion of related work and all proofs of the theoretical results to the appendix.

The contributions of this paper are as follows (Figure 1): 1.

Federated Domain Adaptation (FDA) is a federated learning (FL) approach that improves model performance at the target client by collaborating with source clients while preserving data privacy. FDA faces two primary challenges: domain shifts between source and target data and limited labeled data at the target. Most existing FDA methods focus on domain shifts, assuming ample target data, yet often neglect the combined challenges of both domain shifts and data scarcity. Moreover, approaches that address both challenges fail to prioritize sharing relevant information from source clients according to the target's objective. In this paper, we propose FedDAF, a novel approach addressing both challenges in FDA. FedDAF uses similarity-based aggregation of the global source model and target model by calculating model functional distance from their mean gradient fields computed on target data. This enables effective model aggregation based on the target objective, constructed using target data, even with limited data. While computing model functional distance between these two models, FedDAF computes the angle between their mean gradient fields and then normalizes with the Gompertz function. To construct the global source model, all the local source models are aggregated using simple average in the server. Experiments on real-world datasets demonstrate FedDAF's superiority over existing FL, PFL, and FDA methods in terms of achieving better test accuracy.