Related papers: Nonparametric Generative Modeling with Conditional…

Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of…

Super-resolution is an ill-posed problem, since it allows for multiple predictions for a given low-resolution image. This fundamental fact is largely ignored by state-of-the-art deep learning based approaches. These methods instead train a…

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Graph generation has emerged as a critical task in fields ranging from drug discovery to circuit design. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing…

Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

Time series imputation is important for numerous real-world applications. To overcome the limitations of diffusion model-based imputation methods, e.g., slow convergence in inference, we propose a novel method for time series imputation in…

Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest…

Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore…

Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow-wall coupling challenge deterministic estimation…

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods…

MeanFlow (MF) has recently been established as a framework for one-step generative modeling. However, its ``fastforward'' nature introduces key challenges in both the training objective and the guidance mechanism. First, the original MF's…

The sliced Wasserstein (SW) distance has been widely recognized as a statistically effective and computationally efficient metric between two probability measures. A key component of the SW distance is the slicing distribution. There are…

Score-based Generative Models (SGMs) approximate a data distribution by perturbing it with Gaussian noise and subsequently denoising it via a learned reverse diffusion process. These models excel at modeling complex data distributions and…

We present a generative modeling framework for synthesizing physically feasible two-dimensional incompressible flows under arbitrary obstacle geometries and boundary conditions. Whereas existing diffusion-based flow generators either ignore…

The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is transformed into a Liouville partial differential equation (PDE)-based formalism. First, the stochastic diffusive term from the Fokker-Planck…

Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…

Flow-based generative models show great potential in image synthesis due to its reversible pipeline and exact log-likelihood target, yet it suffers from weak ability for conditional image synthesis, especially for multi-label or unaware…

The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…