用确定性轨迹高效采样复杂分布，15步生成高质量图像
Score-based deterministic density sampling
- 通过实时学习时变得分，构建确定性采样路径
- 仅15步即可生成高质图像，收敛速度达理论最优
- 适合需要稳定、低噪生成的高维数据任务
我们提出一种基于得分的确定性采样框架，仅需目标分布的得分∇log π 即可对未归一化目标密度π进行采样。该方法通过在线学习时变得分∇log f_t，近似KL(f_t∥π)的Wasserstein梯度流。与Langevin动力学具有相同边缘分布，但生成平滑确定性轨迹，实现无噪声单调收敛。理论上证明：在充分训练下，其相对熵耗散速率与精确梯度流一致。数值实验验证：方法以最优速率收敛，轨迹光滑，样本效率常优于随机版本。在高维图像数据上，仅需15步即生成高质量样本，表现出自然探索行为。内存与运行时间随样本量线性增长。
原文摘要 · Abstract (English)
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density $π$ given only its score $\nabla \log π$. Our method approximates the Wasserstein gradient flow on $\mathrm{KL}(f_t\|π)$ by learning the time-varying score $\nabla \log f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.
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