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#