Twist Flow for Inverse Problems

Key points

• In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions.1
• We propose joint twist-flow, an augmented flow-matching formulation that learns a continuous transport from the augmented source state $(zx, y)$ to the augmented terminal state $(x, zy)$.1
• We validate the method on low-dimensional inverse problems with reference posterior samples, where joint twist-flow better preserves multimodal posterior support than a direct conditional-flow baseline.1
• We further evaluate the method on image restoration and seismic subsurface velocity-model inversion, showing increased posterior variability while maintaining observation consistency.1

Sources (1)

• [1]Twist Flow for Inverse Problems
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 01:30 AM

  Direct conditional generative models introduce latent noise to model this ambiguity, but paired inverse-problem training can still encourage an almost deterministic map from the observation to the target.

  In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions.

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