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An Introduction to Flow Matching
Flow matching (FM) is a new generative modelling paradigm which is rapidly gaining popularity in the deep learning community. Flow matching combines aspects ...
The benefit of the CFM loss being that once we define the conditional probability path $p_t(x \mid x_1)$, we can construct an unbiased Monte Carlo estimator of the objective using samples $\big( x_1^{(i)} \big)_{i = 1}^n$ from the data target $q_1$! More generally, samples from the reference distribution which are arbitrarily close to eachothers can be associated with either target modes, leading to high variance in the vector field regression loss. Watson, Joseph L. and Juergens, David and Bennett, Nathaniel R. and Trippe, Brian L. and Yim, Jason and Eisenach, Helen E. and Ahern, Woody and Borst, Andrew J. and Ragotte, Robert J. and Milles, Lukas F. and Wicky, Basile I. M. and Hanikel, Nikita and Pellock, Samuel J. and Courbet, Alexis and Sheffler, William and Wang, Jue and Venkatesh, Preetham and Sappington, Isaac and Torres, Susana V{'a}zquez and Lauko, Anna and De Bortoli, Valentin and Mathieu, Emile and Ovchinnikov, Sergey and Barzilay, Regina and Jaakkola, Tommi S. and DiMaio, Frank and Baek, Minkyung and Baker, David (2023).
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