提出新型生成模型框架，统一解释漂移模型与Wasserstein梯度流关系。
Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences
- 通过KDE近似建立漂移场与Wasserstein-2梯度流的数学等价性。
- 证明漂移场等于KDE对数密度梯度差，实现生成过程理论统一。
- 结合反KL与χ²散度，避免模式崩溃和模糊，适合语义空间建模。
我们揭示了一类新型生成模型——梯度流漂移（Gradient Flow Drifting）的精确数学框架。该框架证明：近期提出的漂移模型（arXiv:2602.04770）在核密度估计（KDE）近似下，等价于前向KL散度的Wasserstein梯度流。具体而言，漂移场在带宽平方缩放后，恰好等于KDE对数密度梯度之差∇log p_kde − ∇log q_kde，即Wasserstein-2梯度流中粒子速度场。此外，该广义框架还包含基于MMD的生成器，作为不同散度在KDE近似下的特例。本文提供简洁可辨识性证明及理论支持的混合散度策略，将反KL与χ²散度梯度流结合，同时避免模式崩溃与模式模糊；进一步扩展至黎曼流形，放宽核函数约束，更适用于语义空间。合成基准上的初步实验验证了该框架的有效性。
原文摘要 · Abstract (English)
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 flow of the forward KL divergence under kernel density estimation (KDE) approximation. Specifically, we prove that the drifting field of drifting model (arXiv:2602.04770) equals, up to a bandwidth-squared scaling factor, the difference of KDE log-density gradients $\nabla \log p_{\mathrm{kde}} - \nabla \log q_{\mathrm{kde}}$, which is exactly the particle velocity field of the Wasserstein-2 gradient flow of $KL(q\|p)$ with KDE-approximated densities. Besides that, this broad family of generative models can also include MMD-based generators, which arises as special cases of Wasserstein gradient flows of different divergences under KDE approximation. We provide a concise identifiability proof, and a theoretically grounded mixed-divergence strategy. We combine reverse KL and $χ^2$ divergence gradient flows to simultaneously avoid mode collapse and mode blurring, and extend this method onto Riemannian manifold which loosens the constraints on the kernel function, and makes this method more suitable for the semantic space. Preliminary experiments on synthetic benchmarks validate the framework.
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