# FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions

arXiv: https://arxiv.org/abs/2603.19331 · HTML: https://mlsanity.com/paper/2603.19331/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 31 of its 80 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 30 of 31)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Learning Robotic Manipulation Policies from Point Clouds with Conditional Flow Matching](https://mlsanity.com/paper/2409.07343/) (2024)
- [FlowSDF: Flow Matching for Medical Image Segmentation Using Distance Transforms](https://mlsanity.com/paper/2405.18087/) (2024)
- [vesselFM: A Foundation Model for Universal 3D Blood Vessel Segmentation](https://mlsanity.com/paper/2411.17386/) (2024)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [Automated generation of 0D and 1D reduced-order models of patient-specific blood flow](https://mlsanity.com/paper/2111.04878/) (2021)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Unsupervised Diffeomorphic Surface Registration and Non-Linear Modelling](https://mlsanity.com/paper/2109.13630/) (2021)
- [Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques](https://mlsanity.com/paper/2312.12361/) (2023)
- [Geometric Uncertainty in Patient-Specific Cardiovascular Modeling with Convolutional Dropout Networks](https://mlsanity.com/paper/2009.07395/) (2020)
- [Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification](https://mlsanity.com/paper/2409.02247/) (2024)
- [svMorph: Interactive geometry-editing tools for virtual patient-specific vascular anatomies](https://mlsanity.com/paper/2210.07087/) (2022)
- [Data-driven generation of 4D velocity profiles in the aneurysmal ascending aorta](https://mlsanity.com/paper/2211.00551/) (2022)
- [A Probabilistic Neural Twin for Treatment Planning in Peripheral Pulmonary Artery Stenosis](https://mlsanity.com/paper/2312.00854/) (2023)
- [Hybrid Physics-Based and Data-Driven Modeling of Vascular Bifurcation Pressure Differences](https://mlsanity.com/paper/2402.15651/) (2024)
- [Bayesian Windkessel calibration using optimized 0D surrogate models](https://mlsanity.com/paper/2404.14187/) (2024)
- [Full-field surrogate modeling of cardiac function encoding geometric variability](https://mlsanity.com/paper/2504.20479/) (2025)
- [Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs](https://mlsanity.com/paper/2506.00947/) (2025)
- [Assessing the performance of correlation-based multi-fidelity neural emulators](https://mlsanity.com/paper/2512.02868/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty quantification in mechanics: A unified Bayesian perspective](https://mlsanity.com/paper/2607.18734/) (2026)

## Abstract (arXiv)

Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of training efforts over clinical targets. However, even the most modern approaches fall short in two important scenarios: open-loop models with known mean flow and assumed waveform shapes, and anatomies affected by vascular lesions where segmentation influences the reachability of pressure or flow split targets. In both cases, boundary conditions cannot be tuned in isolation. We introduce a general amortized inference framework based on probabilistic flow that treats clinical targets, inflow features, and point cloud embeddings of patient-specific anatomies as either conditioning variables or quantities to be jointly estimated. We demonstrate the approach on two patient-specific models: an aorto-iliac bifurcation with varying stenosis locations and severity, and a coronary arterial tree.