Sampling from unnormalized multimodal distributions with limited density evaluations remains a fundamental challenge in machine learning and natural sciences. Successful approaches construct a bridge between a tractable reference and the target distribution. Parallel Tempering (PT) serves as the gold standard, while recent diffusion-based approaches offer a continuous alternative at the cost of neural training. In this work, we introduce Conditional Diffusion Sampling (CDS), a framework that combines these two paradigms. To this end, we derive Conditional Interpolants, a class of stochastic processes whose transport dynamics are governed by an exact, closed-form stochastic differential equation (SDE), requiring no neural approximation. Although these dynamics require sampling from a non-trivial initialization distribution, we show both theoretically and empirically that the cost of this initialization diminishes for sufficiently short diffusion times. CDS leverages this by a two-stage procedure: (1) PT is used to efficiently sample the initial distribution, and then (2) samples are transported via the transport SDE. This combination couples the robust global exploration of PT with efficient local transport. Experiments suggest that CDS has the potential to achieve a superior trade-off between sample quality and density evaluation cost compared to state-of-the-art samplers.

翻译：从具有有限密度评估的未归一化多峰分布中采样仍是机器学习与自然科学领域的基础性挑战。现有成功方法通过在易处理参考分布与目标分布之间构建桥梁实现采样。并行回火（PT）作为黄金标准方法，而近期基于扩散的方法虽需神经网络训练，但提供了连续替代方案。本文提出条件扩散采样（CDS）框架，将上述两种范式相结合。为此，我们推导出条件插值器——一类输运动力学由精确闭式随机微分方程（SDE）控制且无需神经逼近的随机过程。尽管这些动力学需要从非平凡初始化分布进行采样，但理论与实验均表明，对于足够短的扩散时间，该初始化成本可被降低。CDS通过两阶段流程利用这一特性：（1）采用PT高效采样初始分布，随后（2）通过输运SDE迁移样本。这种组合耦合了PT的稳健全局探索与高效局部传输特性。实验表明，相较于现有最优采样器，CDS有望在样本质量与密度评估成本之间取得更优平衡。