# Normalizing flows


📂 model-architectures

## MODEL ARCHITECTURES

# Normalizing flows

Transform a simple distribution into a complex data distribution through a sequence of invertible mappings with tractable Jacobians.

## MENTAL MODEL

A reversible deformation of probability space: data can map to noise and noise can map back to data.

## DATA FLOW

- Data sample

- Invertible transformations

- Simple latent distribution

- Exact change-of-variables likelihood

- Reverse transforms for sampling

## How it trains

Maximum likelihood is optimized exactly under architectural constraints that make inversion and the Jacobian determinant tractable.

## How inference runs

Density evaluation runs data toward the latent; generation samples the base distribution and applies every transform in reverse.

## Strengths

- •
Exact likelihood under the model

- •
Invertible encoding and generation

- •
Useful when density estimation is itself important

## Trade-offs

- •
Invertibility constrains network design

- •
High-dimensional media can require deep, memory-heavy flows

- •
Likelihood does not necessarily track perceived sample quality

## Use it when

- Exact density or reversible transforms are requirements

- The domain fits available invertible architectures

- You will evaluate both likelihood and task utility

## Avoid or challenge it when

- Only perceptual generation quality matters

- Architectural flexibility is more important than exact likelihood

- A simpler discriminative uncertainty method is sufficient

## Illustrative published families

- • Real NVP

- • Glow-style image flows

## Commonly combines with

## PRIMARY REFERENCES

## Model Architectures

## Model Architectures