提出Pawsterior框架，让流匹配更好处理有约束的复杂推断问题。
Pawsterior: Variational Flow Matching for Structured Simulation-Based Inference
- 用双侧变分模型直接融入领域几何约束，提升采样稳定性。
- 在标准基准上分类器两样本检验表现更优，后验拟合更准。
- 首次实现对离散潜结构（如切换系统）的流匹配推断，适用更广。
我们提出Pawsterior，一种改进且扩展的基于模拟的推断（SBI）变分流匹配框架。许多SBI问题涉及受结构约束的后验分布，如受限的物理参数或混合离散-连续变量，但标准流匹配方法通常在无约束空间中操作，导致学习效率低下且难以满足物理约束。本文贡献有二：第一，推广CatFlow的几何归纳偏置，形式化了端点诱导的仿射几何限制，通过双侧变分模型将领域几何直接融入推断过程，提升了采样时的数值稳定性，并在标准SBI基准上通过分类器两样本检验表现证明后验保真度显著提高；第二，更重要的是，该变分参数化使流匹配能处理包含离散潜结构（如切换系统）的SBI任务，而这类问题传统流匹配无法应对。Pawsterior为在更广泛的结构化SBI场景中应用流匹配提供了原则性方案。
原文摘要 · Abstract (English)
We introduce Pawsterior, a variational flow-matching framework for improved and extended simulation-based inference (SBI). Many SBI problems involve posteriors constrained by structured domains, such as bounded physical parameters or hybrid discrete-continuous variables, yet standard flow-matching methods typically operate in unconstrained spaces. This mismatch leads to inefficient learning and difficulty respecting physical constraints. Our contributions are twofold. First, generalizing the geometric inductive bias of CatFlow, we formalize endpoint-induced affine geometric confinement, a principle that incorporates domain geometry directly into the inference process via a two-sided variational model. This formulation improves numerical stability during sampling and leads to consistently better posterior fidelity, as demonstrated by improved classifier two-sample test performance across standard SBI benchmarks. Second, and more importantly, our variational parameterization enables SBI tasks involving discrete latent structure (e.g., switching systems) that are fundamentally incompatible with conventional flow-matching approaches. By addressing both geometric constraints and discrete latent structure, Pawsterior provides a principled way to apply flow-matching in a broader range of structured SBI settings.
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