# NanoFlow: Scalable Normalizing Flows with Sublinear Parameter Complexity

arXiv: https://arxiv.org/abs/2006.06280 · HTML: https://mlsanity.com/paper/2006.06280/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [BigVGAN: A Universal Neural Vocoder with Large-Scale Training](https://mlsanity.com/paper/2206.04658/) (2022)
- [PeriodWave: Multi-Period Flow Matching for High-Fidelity Waveform Generation](https://mlsanity.com/paper/2408.07547/) (2024)
- [BigVSAN: Enhancing GAN-based Neural Vocoders with Slicing Adversarial Network](https://mlsanity.com/paper/2309.02836/) (2023)
- [Multi-Resolution Continuous Normalizing Flows](https://mlsanity.com/paper/2106.08462/) (2021)
- [Distilling the Knowledge from Conditional Normalizing Flows](https://mlsanity.com/paper/2106.12699/) (2021)
- [GMTalker: Gaussian Mixture-based Audio-Driven Emotional Talking Video Portraits](https://mlsanity.com/paper/2312.07669/) (2023)
- [FlowVocoder: A small Footprint Neural Vocoder based Normalizing flow for Speech Synthesis](https://mlsanity.com/paper/2109.13675/) (2021)
- [Kernelised Normalising Flows](https://mlsanity.com/paper/2307.14839/) (2023)
- [Toward Complex-Valued Neural Networks for Waveform Generation](https://mlsanity.com/paper/2603.11589/) (2026)

## Abstract (arXiv)

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter complexity because of reduced expressiveness of bijective mapping, which renders the models unfeasibly expensive in terms of parameters. We present an alternative parameterization scheme called NanoFlow, which uses a single neural density estimator to model multiple transformation stages. Hence, we propose an efficient parameter decomposition method and the concept of flow indication embedding, which are key missing components that enable density estimation from a single neural network. Experiments performed on audio and image models confirm that our method provides a new parameter-efficient solution for scalable NFs with significant sublinear parameter complexity.