  We propose a systematic training-free method to transform the probability
flow of a "linear" stochastic process characterized by the equation
X_{t}=a_{t}X_{0}+\sigma_{t}X_{1} into a straight constant-speed (SC) flow,
reminiscent of Rectified Flow. This transformation facilitates fast sampling
along the original probability flow via the Euler method 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 of two distinct linear
stochastic processes. Moreover, we can easily integrate high-order numerical
solvers into the transformed SC flow, further enhancing the sampling accuracy
and efficiency. Rigorous theoretical analysis and extensive experimental
results substantiate the advantages of our framework. Our code is available at
this [https://github.com/clarken92/VFM||link].
