# Flow to Learn: Flow Matching on Neural Network Parameters

arXiv: https://arxiv.org/abs/2503.19371 · HTML: https://mlsanity.com/paper/2503.19371/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 42 of its 52 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Meta-Baseline: Exploring Simple Meta-Learning for Few-Shot Learning](https://mlsanity.com/paper/2003.04390/) (2020)
- [Supervised Pretraining Can Learn In-Context Reinforcement Learning](https://mlsanity.com/paper/2306.14892/) (2023)
- [Pushing the Limits of Simple Pipelines for Few-Shot Learning: External Data and Fine-Tuning Make a Difference](https://mlsanity.com/paper/2204.07305/) (2022)
- [General-Purpose In-Context Learning by Meta-Learning Transformers](https://mlsanity.com/paper/2212.04458/) (2022)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Graph Neural Networks for Learning Equivariant Representations of Neural Networks](https://mlsanity.com/paper/2403.12143/) (2024)

## Built on by (most cited first, 3 of 3)

- [Position: Weight Space Should Be a First-Class Generative AI Modality](https://mlsanity.com/paper/2605.18632/) (2026)
- [DeepWeightFlow: Re-Basined Flow Matching for Generating Neural Network Weights](https://mlsanity.com/paper/2601.05052/) (2026)
- [NNiT: Width-Agnostic Neural Network Generation with Structurally Aligned Weight Spaces](https://mlsanity.com/paper/2603.00180/) (2026)

## Abstract (arXiv)

Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to generate neural network parameters for different tasks. Our approach models the flow on latent space, while conditioning the process on context data. Experiments verify that FLoWN attains various desiderata for a meta-learning model. In addition, it matches or exceeds baselines on in-distribution tasks, provides better initializations for classifier training, and is performant on out-of-distribution few-shot tasks while having a fine-tuning mechanism to improve performance.