Denoising diffusion networks for normative modeling in neuroimaging

TL;DR

This paper introduces denoising diffusion probabilistic models as a novel approach for normative modeling in neuroimaging, enabling scalable, multivariate, and well-calibrated deviation scores from high-dimensional data.

Contribution

It proposes a unified diffusion-based framework with transformer and MLP backbones for normative modeling, improving calibration and dependence modeling in high-dimensional neuroimaging data.

Findings

Diffusion models achieve well-calibrated outputs comparable to traditional methods in low dimensions.

Transformer backbone better preserves higher-order dependence at high dimensions.

Scalable joint normative models outperform MLP in calibration and dependence preservation.

Abstract

Normative modeling estimates reference distributions of biological measures conditional on covariates, enabling centiles and clinically interpretable deviation scores to be derived. Most neuroimaging pipelines fit one model per imaging-derived phenotype (IDP), which scales well but discards multivariate dependence that may encode coordinated patterns. We propose denoising diffusion probabilistic models (DDPMs) as a unified conditional density estimator for tabular IDPs, from which univariate centiles and deviation scores are derived by sampling. We utilise two denoiser backbones: (i) a feature-wise linear modulation (FiLM) conditioned multilayer perceptron (MLP) and (ii) a tabular transformer with feature self-attention and intersample attention (SAINT), conditioning covariates through learned embeddings. We evaluate on a synthetic benchmark with heteroscedastic and multimodal age effects and on UK Biobank FreeSurfer phenotypes, scaling from dimension of 2 to 200. Our evaluation suite includes centile calibration (absolute centile error, empirical coverage, and the probability integral transform), distributional fidelity (Kolmogorov-Smirnov tests), multivariate dependence diagnostics, and nearest-neighbour memorisation analysis. For low dimensions, diffusion models deliver well-calibrated per-IDP outputs comparable to traditional baselines while jointly modeling realistic dependence structure. At higher dimensions, the transformer backbone remains substantially better calibrated than the MLP and better preserves higher-order dependence, enabling scalable joint normative models that remain compatible with standard per-IDP pipelines. These results support diffusion-based normative modeling as a practical route to calibrated multivariate deviation profiles in neuroimaging.