We introduce a variational inference interpretation for models of "posterior flows" - generalizations of "probability flows" to a broader class of stochastic processes not necessarily diffusion processes. We coin the resulting models as "Variational Flow Models". Additionally, we propose a systematic training-free method to transform the posterior flow of a "linear" stochastic process characterized by the equation Xt = at * X0 + st * X1 into a straight constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation facilitates fast sampling along the original posterior flow without training a new model of the SC flow. The flexibility of our approach allows us to extend our transformation to inter-convert two posterior flows from distinct "linear" stochastic processes. Moreover, we can easily integrate high-order numerical solvers into the transformed SC flow, further enhancing sampling accuracy and efficiency. Rigorous theoretical analysis and extensive experimental results substantiate the advantages of our framework.

翻译：我们提出了一种针对“后向流”模型的变分推断解释——这类模型将“概率流”推广到更广泛的随机过程类别，且不限于扩散过程。我们将由此产生的模型命名为“变分流模型”。此外，我们提出了一种无需训练的系统性方法，可将由方程 Xt = at * X0 + st * X1 描述的“线性”随机过程的后向流转化为直线恒速（SC）流，类似于整流流。这种转换使得我们能够在不训练新的SC流模型的情况下，沿原始后向流实现快速采样。我们方法的灵活性还允许我们将这种转换扩展到两个不同“线性”随机过程的后向流之间的相互转换。此外，我们可以将高阶数值求解器轻松集成到转换后的SC流中，从而进一步提高采样的准确性和效率。严格的理论分析和广泛的实验结果证实了我们框架的优势。