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Normalizing Flows

771 papers tagged archive 2025-07-28

Introduced by Danilo Jimenez Rezende et al. in Variational Inference with Normalizing Flows

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

Normalizing Flows are a method for constructing complex distributions by transforming a probability density through a series of invertible mappings. By repeatedly applying the rule for change of variables, the initial density ‘flows’ through the sequence of invertible mappings. At the end of this sequence we obtain a valid probability distribution and hence this type of flow is referred to as a normalizing flow.

In the case of finite flows, the basic rule for the transformation of densities considers an invertible, smooth mapping f : ℝᵈ →ℝᵈ with inverse f⁻¹ = g, i.e. the composition g ·f(z) = z. If we use this mapping to transform a random variable z with distribution q(z), the resulting random variable z′ = f(z) has a distribution:

q(𝐳′) = q(𝐳)|det(δf⁻¹)/(δ𝐳′)|= q(𝐳)|detδf/δ𝐳|⁻¹ where the last equality can be seen by applying the chain rule (inverse function theorem) and is a property of Jacobians of invertible functions. We can construct arbitrarily complex densities by composing several simple maps and successively applying the above equation. The density q_K(𝐳) obtained by successively transforming a random variable z₀ with distribution q₀ through a chain of K transformations fₖ is:

z_K = f_K ·…·f₂ ·f₁(z₀)

lnq_K(z_K) = lnq₀(z₀) − ∑ᴷₖ₌₁ln|δfₖ/(δ𝐳ₖ₋₁)| The path traversed by the random variables zₖ = fₖ(zₖ₋₁) with initial distribution q₀(z₀) is called the flow and the path formed by the successive distributions qₖ is a normalizing flow.

PaperSourceSee Code · ex4sperans/variational-inference-with-normalizing-flows

Papers archive 2025-07-28

30 shown of 771, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 367 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
Density Estimation76
Variational Inference54
Image Generation37
Anomaly Detection29
Text to Speech26
text-to-speech26
Uncertainty Quantification24
Time Series23
Speech Synthesis22
Bayesian Inference18
Denoising18
regression17
Out-of-Distribution Detection16
Time Series Analysis16
Decision Making15
Gaussian Processes15
Reinforcement Learning (RL)15
Decoder14
Representation Learning14
reinforcement-learning14

Usage over time archive 2025-07-28

Papers per year tagged with Normalizing Flows: 2015 to 2025, peak 139 139 0 2015: 7 papers 2015 2016: 13 papers 2016 2017: 25 papers 2017 2018: 30 papers 2018 2019: 69 papers 2019 2020: 100 papers 2020 2021: 115 papers 2021 2022: 106 papers 2022 2023: 139 papers 2023 2024: 110 papers 2024 2025: 57 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (771 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Distribution Approximation

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