# One Evaluation, Any Operating Point: Hypernetwork-Amortized MeanFlow for 3D MRI Reconstruction

arXiv: https://arxiv.org/abs/2609.31655 · HTML: https://mlsanity.com/paper/2609.31655/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [The 2024 Brain Tumor Segmentation (BraTS) Challenge: Glioma Segmentation on Post-treatment MRI](https://mlsanity.com/paper/2405.18368/) (2024)
- [Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition](https://mlsanity.com/paper/1902.03051/) (2019)
- [Active MR k-space Sampling with Reinforcement Learning](https://mlsanity.com/paper/2007.10469/) (2020)
- [SKM-TEA: A Dataset for Accelerated MRI Reconstruction with Dense Image Labels for Quantitative Clinical Evaluation](https://mlsanity.com/paper/2203.06823/) (2022)
- [Learning-based Optimization of the Under-sampling Pattern in MRI](https://mlsanity.com/paper/1901.01960/) (2019)
- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [Learning-Based Compressive MRI](https://mlsanity.com/paper/1805.01266/) (2018)
- [Computing Multiple Image Reconstructions with a Single Hypernetwork](https://mlsanity.com/paper/2202.11009/) (2022)

## Abstract (arXiv)

Generative priors reconstruct accelerated 3D MRI well but pay heavily at deployment: tens of network evaluations per volume, and protocol-specific hyperparameter tuning. A third hidden cost is the scanner's fixed sampling pattern. We treat the whole operating point as an input. A 3D MeanFlow patch network (a one-step flow model) is fine-tuned end-to-end through a warm-started, five-iteration differentiable conjugate-gradient projection. A small hypernetwork maps the operating point (data-consistency weight, acceleration, and the Cartesian sampling pattern itself) to the network's per-channel modulation. Three findings follow. (i) Learning the acquisition is worth more than any other operating point: on clinical knee data, the learned mask gains up to +2.34 dB over the protocol's variable-density mask. This gain requires the solver: with a feed-forward reconstructor the same learned mask hurts at 4x (-1.7 dB), but with the data-consistency projection it adds +4.6 dB. (ii) One evaluation is highly effective: it beats a 20-step patch-diffusion prior by up to +3.1 dB on brain and +2.9 dB on knee. Three to five evaluations extend the front to +6 dB while using a quarter of the prior's network calls. (iii) Fully sampled targets are optional: trained self-supervised on a split of acquired samples, the reconstructor matches its supervised twin at 4x on real data. Finally, we report what failed and why: subject-adaptive acquisition from measured energy, combining self-supervision with learned acquisition, and amortising the data-consistency weight.