# ReMiDi: Reconstruction of Microstructure Using a Differentiable Diffusion MRI Simulator

arXiv: https://arxiv.org/abs/2502.01988 · HTML: https://mlsanity.com/paper/2502.01988/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 37 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [xi-torch: differentiable scientific computing library](https://mlsanity.com/paper/2010.01921/) (2020)
- [A generative model of realistic brain cells with application to numerical simulation of diffusion-weighted MR signal](https://mlsanity.com/paper/1806.07125/) (2018)

## Built on by (most cited first, 2 of 2)

- [Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI](https://mlsanity.com/paper/2603.04638/) (2026)
- [PRISM: Differentiable Analysis-by-Synthesis for Fixel Recovery in Diffusion MRI](https://mlsanity.com/paper/2604.00250/) (2026)

## Abstract (arXiv)

We propose ReMiDi, a novel method for inferring neuronal microstructure as arbitrary 3D meshes using a differentiable diffusion Magnetic Resonance Imaging (dMRI) simulator. We first implemented in PyTorch a differentiable dMRI simulator that simulates the forward diffusion process using a finite-element method on an input 3D microstructure mesh. To achieve significantly faster simulations, we solve the differential equation semi-analytically using a matrix formalism approach. Given a reference dMRI signal Sref, we use the differentiable simulator to iteratively update the input mesh such that it matches Sref using gradient-based learning. Since directly optimizing the 3D coordinates of the vertices is challenging, particularly due to ill-posedness of the inverse problem, we instead optimize a lower-dimensional latent space representation of the mesh. The mesh is first encoded into spectral coefficients, which are further encoded into a latent z using an auto-encoder, and are then decoded back into the true mesh. We present an end-to-end differentiable pipeline that simulates signals that can be tuned to match a reference signal by iteratively updating the latent representation z. We demonstrate the ability to reconstruct microstructures of arbitrary shapes represented by finite-element meshes, with a focus on axonal geometries found in the brain white matter, including bending, fanning and beading fibers. Our source code is available online.