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Program-space Diffusion for Morphology-to-Transcriptomics Prediction
Ruyter Swann, Dorent Reuben, Racoceanu Daniel
TL;DR
Predicting spatial transcriptomics from histology is costly and difficult because existing methods often predict genes independently. This paper uses cNMF transcriptional programs with conditional diffusion, achieving comparable or better predictive performance while making sampling nearly independent of gene-panel size.
Problem
Spatial transcriptomics is costly and difficult to acquire, while existing morpho-transcriptomic methods face normalization sensitivity and poor scalability in high-dimensional gene space.
Method
The model normalizes expression with Pearson residuals and uses conditional diffusion in a fixed, low-dimensional cNMF program space.
Results
Program-space diffusion yields comparable or better Top-M performance than gene-space diffusion while keeping sampling nearly independent of gene-panel size.
Takeaways & Limitations
Program-space diffusion offers a scalable alternative for morphology-to-transcriptomics prediction under controlled normalization.
Takeaways & Limitations
Reconstruction through the fixed cNMF basis does not recover expression components outside the learned subspace.
Abstract
from arXiv · showhide
Spatial transcriptomics (ST) enables genome-wide gene expression profiling while preserving tissue architecture, but its cost and limited scalability remain major bottlenecks. This has motivated models that predict spatial expression directly from routine histology. Despite promising results, most existing approaches operate at the gene level without leveraging established transcriptomic modeling practices and rely on heterogeneous gene selection strategies, which complicates fair comparison across methods. We propose to reformulate morphology-to-transcriptomics prediction as conditional generation in transcriptional program space, thereby exploiting coordinated transcriptional variation instead of predicting genes independently. Using consensus non-negative matrix factorization (cNMF), we extract a low-dimensional set of transcriptional programs capturing coordinated expression variation in the training data, and train a conditional diffusion model to generate program activations from histology. This formulation exploits coordinated transcriptional variation and substantially lowers the dimensionality of the conditional generative task.
1 Introduction
The introduction frames morphology-to-transcriptomics prediction as a challenging, non-unique task affected by noisy spatial transcriptomics measurements. It motivates a reformulation in transcriptional program space alongside Pearson-residual normalization to address limitations of existing diffusion-based inference.
- Motivation: Spatial transcriptomics links H&E morphology with spatially resolved gene expression while preserving tissue architecture.This joint view enables morphological patterns in whole-slide imaging to be interpreted alongside transcriptional variation.
- Challenges: Prediction is difficult because spatial transcriptomics measurements are noisy and technology-dependent, while morphology does not uniquely determine expression.Sources of measurement variation include sequencing depth, technical noise, dropouts, and sectioning or image–spot alignment artifacts.
- Prior work: Early models used supervised regression from spot-centered H&E patches to gene-expression vectors, followed by CNN, Transformer, and graph-based architectural extensions.These developments aimed to exploit multi-scale tissue context and spatial reasoning but did not account for the non-uniqueness of the morphology–expression relationship.
- Contributions: The work addresses diffusion-based inference limitations through Pearson-residual normalization and a reformulation of prediction in transcriptional program space.Pearson residuals account for sequencing depth and UMI count mean–variance relationships, producing approximately variance-stabilized representations unlike standard log-based preprocessing.
2 Method
The method normalizes spatial transcriptomics counts with Pearson residuals, derives consensus transcriptional programs using cNMF, and trains a conditional DDPM to predict program activations from histology. Gene expression is reconstructed through a fixed consensus basis, reducing the diffusion target from gene space to a lower-dimensional program space.
- Normalization: Pearson-residual normalization accounts for spot-specific sequencing depth and UMI count mean–variance relationships, reducing technical variability before downstream modeling.Residuals are approximately variance-stabilized across genes and expression levels; residuals are clipped and globally shifted to satisfy non-negativity requirements.
- Program extraction: cNMF extracts coordinated transcriptional programs within each training fold, representing each spot as a non-negative combination of program loadings.Consensus programs are formed by clustering normalized loadings across independent NMF runs and averaging loadings within clusters.
- Program extraction: K = 20 is selected as a compact operating point balancing reconstruction fidelity, activation sparsity, and target dimensionality across K ∈{10, 20, 40, 60, 100}.Increasing K improved oracle reconstruction quality but produced denser per-spot activations; K = 20 is not interpreted as biologically optimal or universally transferable.
- Program-space diffusion: The conditional DDPM operates on program activations in R^K rather than genes in R^G, with K ≪G, while conditioning denoising on noisy activations, histology patches, and diffusion timesteps.The fixed consensus basis constrains predictions to coordinated transcriptional programs and remains unchanged during diffusion training.
- Reconstruction: At inference, generated program activations are projected back to gene space through the fixed training-fold cNMF basis, without implying recovery outside that subspace.The diffusion model predicts only the low-dimensional activation coefficients H, while expression is approximated within the subspace spanned by W∗.
3 Experiments
Experiments evaluate the framework on HER2-positive breast cancer spatial transcriptomics data using matched histology and gene-expression measurements. Results assess normalization, predictive performance across gene-panel sizes, and computational scalability of program-space versus gene-space diffusion.
- Dataset: The evaluation uses 35 quality-controlled tissue sections from eight patients, with approximately 300–700 spots per slide and paired H&E whole-slide images, coordinates, and spot-level expression.The cohort originally contains 36 sections, with one removed during quality control.
- Normalization: The study compares log normalization with Pearson-residual normalization because normalization affects gene-level metrics and may confound method comparisons.STEM retains its original element-wise log2(X + 1) transformation in Protocol A, while Protocol B uses Pearson residuals.
- Predictive performance: Under fixed Pearson normalization, program-space diffusion produces modest but consistent improvements over the STEM gene-space baseline across reported Top-M PCC thresholds.The cNMF Oracle NNLS is included as a reconstruction upper bound rather than a predictive model.
- Predictive performance: Increasing the gene panel from G=300 to G=800 and G=2000 significantly improves per-slide Top-50 PCC for both gene-space and program-space diffusion.Figure 1 reports patient-held-out distributions and paired Wilcoxon signed-rank significance testing.
- Computation scalability: Sampling throughput in gene-space falls from 27.3 it/s at G=300 to 7.4 it/s at G=800 and 1.7 it/s at G=2000, whereas program-space scales favorably with larger panels.At G=800 and G=2000, gene-space requires approximately 2 min 15 s and 36 min per 1,000 diffusion steps, respectively.
4 Conclusion
The conclusion identifies normalization as a first-order determinant of reported accuracy and contrasts gene-space diffusion’s inference cost with cNMF program-space diffusion’s comparable or better Top-M performance under controlled normalization.
- Normalization is a first-order determinant of reported accuracy because replacing STEM’s log normalization with Pearson residuals changes the prediction target representation and Top-M PCC.
- Larger gene panels improve per-slide predictive quality, but gene-space diffusion becomes prohibitively expensive at inference.
- Diffusion in cNMF program space achieves comparable or better Top-M performance under controlled normalization than gene-space diffusion.