MorphoFlow: Sparse-Supervised Generative Shape Modeling with Adaptive Latent Relevance

Mokshagna Sai Teja Karanam; Tushar Kataria; Shireen Elhabian

cs.CVApr 13, 2026

MorphoFlow: Sparse-Supervised Generative Shape Modeling with Adaptive Latent Relevance

Authors: Mokshagna Sai Teja Karanam, Tushar Kataria, Shireen Elhabian

Organizations: Kahlert School of Computing, Scientific Computing and Imaging Institute, University of Utah, Utah, USA

Abstract

Statistical shape modeling (SSM) is central to population level analysis of anatomical variability, yet most existing approaches rely on densely annotated segmentations and fixed latent representations. These requirements limit scalability and reduce flexibility when modeling complex anatomical variation. We introduce MorphoFlow, a sparse supervised generative shape modeling framework that learns compact probabilistic shape representations directly from sparse surface annotations. MorphoFlow integrates neural implicit shape representations with an autodecoder formulation and autoregressive normalizing flows to learn an expressive probabilistic density over the latent shape space. The neural implicit representation enables resolution-agnostic modeling of 3D anatomy, while the autodecoder formulation supports direct optimization of per-instance latent codes under sparse supervision. The autoregressive flow captures the distribution of latent anatomical variability providing a tractable, likelihood-based generative model of shapes. To promote compact and structured latent representations, we incorporate adaptive latent relevance weighting through sparsity-inducing priors, enabling the model to regulate the contribution of individual latent dimensions according to their relevance to the underlying anatomical variation while preserving generative expressivity. The resulting latent space supports uncertainty quantification and anatomically plausible shape synthesis without manual latent dimensionality tuning. Evaluation on publicly available lumbar vertebrae and femur datasets demonstrates accurate high-resolution reconstruction from sparse inputs and recovery of structured modes of anatomical variation consistent with population level trends.

Figures & tables

Figure 1: MorphoFlow Architecture . For only generative shape modelling $\alpha^{-1}=1$ , making the distribution a standard normal. For compact shape latent $\alpha^{-1}$ values are learned during training with ARD regularization loss.

		MorphoFlow w/o flow				MorphoFlow
	Dim	ASD $\downarrow$	HSD95 $\downarrow$	HSD $\downarrow$	DSC $\uparrow$	ASD $\downarrow$	HSD95 $\downarrow$	HSD $\downarrow$	DSC $\uparrow$	Var	R 2 -Corr
Thin	16	$0.86_{\pm 0.25}$	$3.41_{\pm 1.34}$	$9.86_{\pm 3.05}$	$0.87_{\pm 0.03}$	$0.84_{\pm 0.25}$	$3.41_{\pm 1.62}$	$9.96_{\pm 4.00}$	$0.87_{\pm 0.03}$	11-12-13	0.76-0.87
	32	$0.69_{\pm 0.18}$	$2.75_{\pm 1.01}$	$8.62_{\pm 2.76}$	$0.89_{\pm 0.02}$	$0.72_{\pm 0.25}$	$3.04_{\pm 1.51}$	$9.16_{\pm 3.19}$	$0.89_{\pm 0.02}$	20-21-23	0.72-0.85
	64	$0.57_{\pm 0.16}$	$2.38_{\pm 1.07}$	$8.05_{\pm 3.03}$	$0.91_{\pm 0.02}$	$0.60_{\pm 0.23}$	$2.64_{\pm 1.28}$	$8.53_{\pm 3.5}$	$0.90_{\pm 0.03}$	39-44-46	0.79-0.89
	128	$0.49_{\pm 0.13}$	$2.15_{\pm 0.69}$	$7.78_{\pm 2.47}$	$0.92_{\pm 0.02}$	$0.55_{\pm 0.23}$	$2.57_{\pm 1.28}$	$8.49_{\pm 3.98}$	$0.91_{\pm 0.02}$	69-79-85	0.33-0.58
	256	$0.73_{\pm 0.11}$	$1.91_{\pm 0.55}$	$7.12_{\pm 2.22}$	$0.93_{\pm 0.01}$	$0.59_{\pm 0.27}$	$2.74_{\pm 1.52}$	$9.17_{\pm 3.78}$	$0.91_{\pm 0.03}$	164-174-183	0.45-0.67

Table 1: Quantitative Results on VERSE. Average Surface Distance ( ASD ), Hausdorff Distance ( HSD , HSD95 ), and Dice Score ( DSC ) are reported for all models. Var denotes the number of latent dimensions explaining 95–97–99% variance after ARD regularization. R 2 and Corr (Pearson r) evaluate predictive performance.

		MorphoFlow w/o flow				MorphoFlow
	Dim	ASD $\downarrow$	HSD95 $\downarrow$	HSD $\downarrow$	DSC $\uparrow$	ASD $\downarrow$	HSD95 $\downarrow$	HSD $\downarrow$	DSC $\uparrow$	Var	R 2
Thin	16	$1.82_{\pm 0.47}$	$5.42_{\pm 1.40}$	$13.80_{\pm 3.83}$	$0.94_{\pm 0.01}$	$1.14_{\pm 0.25}$	$3.55_{\pm 0.82}$	$10.65_{\pm 3.64}$	$0.96_{\pm 0.01}$	11-12-13	0.69-0.83
	32	$1.21_{\pm 0.27}$	$3.79_{\pm 0.89}$	$10.85_{\pm 3.02}$	$0.96_{\pm 0.01}$	$0.87_{\pm 0.19}$	$2.82_{\pm 0.65}$	$9.30_{\pm 3.08}$	$0.97_{\pm 0.00}$	20-22-24	0.55-0.74
	64	$0.84_{\pm 0.17}$	$2.75_{\pm 0.60}$	$9.13_{\pm 3.26}$	$0.97_{\pm 0.00}$	$0.70_{\pm 0.15}$	$2.35_{\pm 0.55}$	$8.64_{\pm 2.87}$	$0.98_{\pm 0.00}$	39-44-47	0.68-0.82
	128	$0.64_{\pm 0.12}$	$2.19_{\pm 0.46}$	$8.14_{\pm 2.53}$	$0.98_{\pm 0.00}$	$0.64_{\pm 0.26}$	$2.18_{\pm 0.91}$	$8.14_{\pm 2.95}$	$0.98_{\pm 0.01}$	76-85-91	0.62-0.79
	256	$0.55_{\pm 0.10}$	$1.90_{\pm 0.42}$	$7.39_{\pm 2.56}$	$0.98_{\pm 0.00}$	$0.64_{\pm 0.35}$	$2.22_{\pm 1.09}$	$8.24_{\pm 3.19}$	$0.98_{\pm 0.01}$	163-176-186	0.55-0.74

Table 2: Quantitative Results for Femur.

Figure 2: Results. (A) Best, median, and worst surface reconstructions obtained from models trained on thin, thick, and orthogonal slices(latent dimension=64). The right column shows models trained with MorphoFlow , while the left column shows models trained without Flow and ARD regularization. (B) Estimated $\sigma$ values across different latent dimensionalities when using MorphoFlow showing the impact of ARD regularization. (C) Correlation plots for 1500 generated samples, showing the relationship between the distance in $z_{0}$ space to the nearest training sample and the corresponding surface distance to the closest training surface. (D) Uncertainty visualization for one sample from the VERSE and OAI datasets using the best-performing thin-slice model(64 latent dimention), including a 3D rendering of uncertainty and cross-sectional views in the axial, sagittal, and coronal planes. (E) Generated Shapes from VERSE and OAI models trained with latent dimension 64.

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Guoqing Zhang, Jingyun Yang, Siqi Chen +2

Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · Pengcheng Laboratory, Shenzhen, China · School of AI, Chinese University of Hong Kong (Shenzhen)

3D Shape Generation Latent Diffusion Models

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Oct 20, 2026

TokenFlow: Latent Token Rectified Flow Matching for 3D Point Cloud Generation

3D point clouds generation requires capturing both part-level layout and surface detail while preserving permutation equivariance. Existing latent generative models often encode an entire shape into a single vector, which limits their ability to retain part-level structure. We propose TokenFlow, a hierarchical flow matching framework that represents each shape as a set of latent tokens and couples a rectified flow over these tokens with a conditional flow over points. A bottleneck of

M \ll N

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Polytechnique Montréal, Canada · Mila - Quebec AI Institute, Canada · CHUM - University of Montreal Hospital, Canada

3D Reconstruction 3D Medical Imaging Statistical Shape Modeling

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Abstract

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