Related papers: Drifting Fields are not Conservative
We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because…
Generative Modeling via Drifting has recently achieved state-of-the-art one-step image generation through a kernel-based drift operator, yet the success is largely empirical and its theoretical foundations remain poorly understood. In this…
We propose and analyze a conservative drifting method for one-step generative modeling. The method replaces the original displacement-based drifting velocity by a kernel density estimator (KDE)-gradient velocity, namely the difference of…
Drifting models train one-step generators by optimizing a kernel-induced mean-shift discrepancy between the data and model distributions, with Laplace kernels used by default in practice. At each point, this discrepancy compares the…
We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an…
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…
This paper studies the identifiability and stability of drifting fields within the framework of Generative Modeling via Drifting. The motivating question is whether a zero-drift equilibrium identifies the target distribution, and whether an…
Modern problems in AI or in numerical analysis require nonsmooth approaches with a flexible calculus. We introduce generalized derivatives called conservative fields for which we develop a calculus and provide representation formulas.…
The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized gradients called "conservative fields", defined through the…
Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and…
The drift method, introduced by the second author, provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly…
Traditional analyses of gradient descent optimization show that, when the largest eigenvalue of the loss Hessian - often referred to as the sharpness - is below a critical learning-rate threshold, then training is 'stable' and training loss…
We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient…
We propose Drifting Field Policy (DFP), a non-ODE one-step generative policy built on the drifting model paradigm. We frame the policy update as a reverse-KL Wasserstein-2 gradient flow toward a soft target policy, so that each DFP update…
Drifting Models have emerged as a new paradigm for one-step generative modeling, achieving strong image quality without iterative inference. The premise is to replace the iterative denoising process in diffusion models with a single…
Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…
Discontinuities in spatial derivatives appear in a wide range of physical systems, from creased thin sheets to materials with sharp stiffness transitions. Accurately modeling these features is essential for simulation but remains…
Learning from data streams is an increasingly important topic in data mining, machine learning, and artificial intelligence in general. A major focus in the data stream literature is on designing methods that can deal with concept drift, a…
Recently, Gaussian splatting has emerged as a robust technique for representing 3D scenes, enabling real-time rasterization and high-fidelity rendering. However, Gaussians' inherent radial symmetry and smoothness constraints limit their…
Recently, discriminatively learned correlation filters (DCF) has drawn much attention in visual object tracking community. The success of DCF is potentially attributed to the fact that a large amount of samples are utilized to train the…