# Neural Orientation Distribution Fields for Estimation and Uncertainty Quantification in Diffusion MRI

arXiv: https://arxiv.org/abs/2307.08138 · HTML: https://mlsanity.com/paper/2307.08138/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2023.

## Built on by (most cited first, 6 of 6)

- [Learning Spatially-Continuous Fiber Orientation Functions](https://mlsanity.com/paper/2312.05721/) (2023)
- [Estimating Neural Orientation Distribution Fields on High Resolution Diffusion MRI Scans](https://mlsanity.com/paper/2409.09387/) (2024)
- [CINeMA: Conditional Implicit Neural Multi-Modal Atlas for a Spatio-Temporal Representation of the Perinatal Brain](https://mlsanity.com/paper/2506.09668/) (2025)
- [Implicit neural representations for accurate estimation of the standard model of white matter](https://mlsanity.com/paper/2506.15762/) (2025)
- [SIINR: Structurally Informed Implicit Neural Representations for super-resolution with uncertainty quantification of clinical quality diffusion MRI datasets](https://mlsanity.com/paper/2607.19943/) (2026)
- [Prior-Guided Implicit Neural Representations for Single-Subject Diffusion MRI Super-Resolution](https://mlsanity.com/paper/2609.00981/) (2026)

## Abstract (arXiv)

Inferring brain connectivity and structure textitin-vivo requires accurate estimation of the orientation distribution function (ODF), which encodes key local tissue properties. However, estimating the ODF from diffusion MRI (dMRI) signals is a challenging inverse problem due to obstacles such as significant noise, high-dimensional parameter spaces, and sparse angular measurements. In this paper, we address these challenges by proposing a novel deep-learning based methodology for continuous estimation and uncertainty quantification of the spatially varying ODF field. We use a neural field (NF) to parameterize a random series representation of the latent ODFs, implicitly modeling the often ignored but valuable spatial correlation structures in the data, and thereby improving efficiency in sparse and noisy regimes. An analytic approximation to the posterior predictive distribution is derived which can be used to quantify the uncertainty in the ODF estimate at any spatial location, avoiding the need for expensive resampling-based approaches that are typically employed for this purpose. We present empirical evaluations on both synthetic and real in-vivo diffusion data, demonstrating the advantages of our method over existing approaches.