Score-Based Deterministic Density Sampling

We propose and analyze a deterministic sampling framework using Score-Based Transport Modeling (SBTM) for sampling an unnormalized target density $\pi$. While diffusion generative modeling relies on pre-training the score function $\nabla \log f_t$ using samples from $\pi$, SBTM addresses the more general and challenging setting where only $\nabla \log\pi$ is known. SBTM approximates the Wasserstein gradient flow on KL$(f_t\|\pi)$ by learning the time-varying score $\nabla \log f_t$ on the fly using score matching. The learned score gives immediate access to relative Fisher information, providing a built-in convergence diagnostic. The deterministic trajectories are smooth, interpretable, and free of Brownian-motion noise, while having the same distribution as ULA. We prove that SBTM dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. We further extend our framework to annealed dynamics, to handle non log-concave targets. Numerical experiments validate our theoretical findings: SBTM converges at the optimal rate, has smooth trajectories, and is easily integrated with annealed dynamics. We compare to the baselines of ULA and annealed ULA.

REALEDIT: Reddit Edits As a Large-scale Empirical Dataset for Image Transformations

Existing image editing models struggle to meet real-world demands. Despite excelling in academic benchmarks, they have yet to be widely adopted for real user needs. Datasets that power these models use artificial edits, lacking the scale and ecological validity necessary to address the true diversity of user requests. We introduce REALEDIT, a large-scale image editing dataset with authentic user requests and human-made edits sourced from Reddit. REALEDIT includes a test set of 9300 examples to evaluate models on real user requests. Our results show that existing models fall short on these tasks, highlighting the need for realistic training data. To address this, we introduce 48K training examples and train our REALEDIT model, achieving substantial gains - outperforming competitors by up to 165 Elo points in human judgment and 92 percent relative improvement on the automated VIEScore metric. We deploy our model on Reddit, testing it on new requests, and receive positive feedback. Beyond image editing, we explore REALEDIT's potential in detecting edited images by partnering with a deepfake detection non-profit. Finetuning their model on REALEDIT data improves its F1-score by 14 percentage points, underscoring the dataset's value for broad applications.

Transport based particle methods for the Fokker-Planck-Landau equation

We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method can preserve some important physical properties of the Landau equation, such as the conservation of mass, momentum, and energy, and decay of estimated entropy. We prove that matching the gradient of the logarithm of the approximate solution is enough to recover the true solution to the Landau equation with Maxwellian molecules. Several numerical experiments in low and moderately high dimensions are performed, with particular emphasis on comparing the proposed method with the traditional particle or blob method.