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Normalizing flows

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Normalizing flows are probabilistic generative models where we assume the one-to-one mapping, a bijection, between 𝑝 ( 𝑧 ) p(z) and 𝑝 ( 𝑥 ) p(x), the distribution of latent variables and data. If we choose 𝑝 ( 𝑧 ) p(z) to be a simple base distribution from which we can easily draw samples, due to the connection between them, we can easily calculate the likelihood of data 𝑝 ( 𝑥 ) p(x)​ applying the formula for a change of variables: The absolute determinant of the Jacobian is crucial in connecting these two distributions. A transformation maps an event from one region in the latent space 𝑧 z to another region in the data space 𝑥 x. Due to a bijection, the same number of infinitely many small fragments exists in both regions. However, two regions often differ in size, meaning the corresponding fragments 𝑑 𝑧 dz and 𝑑 𝑥 dx cannot be of the same size, even though they are infinitesimally small. The determinant of the Jacobian measures the change in size of these fragme

Normalizing flows Normalizing flows Published 23 May 2024 Author Rafał Rolczyński Normalizing flows are probabilistic generative models where we assume the one-to-one mapping, a bijection, between $p(\v z)$ and $p(\v x)$, the distribution of latent variables and data. If we choose $p(\v z)$ to be a simple base distribution from which we can easily draw samples, due to the connection between them, we can easily calculate the likelihood of data $p(\v x)$​ applying the formula for a change of variables: \[p(\v x) = \left| \frac{\part \v x}{\part \v z} \right|^{-1} p(\v z)\] The absolute determina

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