SAR-to-EO image translation aims to generate electro-optical (EO) imagery from synthetic aperture radar (SAR) observations. Existing latent diffusion approaches typically inherit a predetermined autoencoder, although reconstruction fidelity can vary substantially across codecs and modalities. Because the latent codec affects the round-trip preservation of both SAR conditions and EO targets, codec selection constitutes a fundamental design choice; nevertheless, existing methods largely rely on codecs pretrained on natural images. To remedy this, we introduce ReFlowSET, a conditional latent flow-matching framework that selects its codec through a joint SAR--EO reconstruction audit. Rather than inheriting a heavyweight pretrained generator, ReFlowSET trains a substantially smaller conditional DiT from scratch in the selected latent space, using dual-stream SAR conditioning followed by joint feature refinement. To provide semantic guidance for this from-scratch training, intermediate noisy-EO features are aligned with clean target-EO representations extracted by a frozen vision foundation model. This alignment is used only during training and introduces no additional inference cost. Experiments on QXS-SAROPT and SAR2Opt demonstrate state-of-the-art performance across diverse perceptual fidelity and distributional metrics. Code and pretrained weights are publicly available at https://github.com/KAIST-VICLab/ReFlowSET.
Generating high-quality 3D point clouds requires capturing both global shape topology and local geometric details. Existing flow-based methods rely on continuous normalizing flows (CNFs) that demand expensive ODE solving and trace estimation during training, while diffusion models require hundreds of iterative denoising steps. Moreover, most approaches adopt single-level generation directly in point space, disregarding the hierarchical structure natural to 3D shapes. We propose Hierarchical Flow Matching (HFM) that extends flow matching to bilevel structure for unconditional 3D point cloud generation. HFM decomposes the task into two levels via optimal-transport flow matching: a \textit{Latent Flow Matching} models the global shape manifold in a compact latent space, and a \textit{Conditional Point Flow Matching} reconstructs detailed point clouds conditioned on the latent code. Both flows are trained with simple MSE regression losses. The resulting straight OT paths enable efficient sampling with as few as 15 Euler steps per flow, while the structured latent space supports downstream tasks including classification. Extensive experiments on ShapeNet and ModelNet benchmarks demonstrate that HFM achieves competitive or even best performance compared with prior state-of-the-art methods.
AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations. Learning a direct mapping from load conditions to OPF solutions can accelerate this computation, yet with deepening renewable penetration, a single optimal dispatch is no longer sufficient. Operators require a characterization of the distribution of feasible near-optimal solutions for risk quantification, sensitivity analysis, and multi-objective trade-off assessment. Supervised neural networks provide fast point predictions but cannot capture this conditional distribution. Diffusion-based generative models can sample diverse solutions in principle, yet existing methods operating in the raw state space exhibit degraded solution quality and fail to scale beyond medium-sized systems. We identify the root cause as the conflation of two distinct tasks within a single model. Compressing the high-dimensional OPF solution manifold is one task, and learning the conditional mapping from loads to that manifold is another. This paper presents FMOPF, a framework that resolves this conflation by decoupling compression from generation through latent flow matching and by explicitly modeling load-state coupling through a Constraint-Aware Interaction Prior Network. Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts, achieves the lowest tail risk among generative methods, and is the first such method to scale to systems with several hundred buses while preserving full feasibility. Ablation studies confirm that the latent generation pipeline is a necessary condition for physical feasibility and that the interaction prior functions as a late-stage tail-risk controller.
Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.