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.

我们提出了“变分流模型”作为“后验流”的广义概率流模型的变分推断解释，并提出了一种无需训练的方法来将“线性”随机过程的后验流转化为直速常数速度（SC）流，便于沿着原始后验流进行快速采样。我们的方法的灵活性允许我们在不同的“线性”随机过程中进行两个后验流的相互转换，同时可以轻松地将高阶数值解算器集成到转换后的SC流中，进一步提高采样精度和效率。严格的理论分析和大量的实验结果证实了我们的框架的优势。

变分流模型：奔流于您的风格