LF M (θ) = Et,pt(x)||ut(x) − vt(x; θ)||2,

4

as(cid:82) pt(x | x1)q(x1)dx1, which closely approximates q(x1) at t = 1. With that, [Lipman et al.,

2023] presents the Conditional Flow Matching (CFM) objective,

LCF M (θ) = Et,q(x1),pt(x|x1)||ut(x | x1) − vt(x; θ)||2.

(4)
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