Dominic Rigby

A Visual Dive into Conditional Flow Matching

Date: 29th October 2026

Blog Post

Related: π0.5: a Vision-Language-Action Model with Open-World Generalization

Generative Modelling

• Three bottlenecks of generative modelling:
  • Sample speed
  • Quality
  • Fully cover underlying distribution p
• Typical strategy: sample from simple base distribution and learn to map it to complex one. Sample x from p, and then learned function
• Learn to maximimise the likelihood that p and T are close in sense of KL divergence

Conditional Flow Matching

• Goal: find velocity field such that p flows through it and ends up as p_desired (check article for intuitive graphics)
• We want to get a supervision signal for every intermediate between t = [0, 1], however there are infinite ways to flow p to p_desired. Therefore, we must learn to specify full vector field

• This is very hard as p_desired is unknown

• Core idea of CFM is to choose a conditioning variable z and a conditional probability p(x

  t,z) such that global p(x

  t) trasnform p_0 into p_desired and that the assosciate veclotiy field has analytical form.