HaDM-ST: Histology-Assisted Spatial Transcriptomics

• HaDM-ST is a high-resolution spatial transcriptomics framework that integrates H&E images and low-resolution data to capture gene-specific spatial patterns.
• It employs a conditional diffusion backbone with semantic distillation and cross-modal spatial alignment to enhance spatial fidelity and modality coherence.
• The framework uses gene-wise differential adversarial learning to maintain inter-gene relationships, achieving improved RMSE and SSIM metrics over baseline methods.

HaDM-ST, short for Histology-Assisted Differential Modeling for Spatial Transcriptomics Generation, is a high-resolution spatial transcriptomics generation framework conditioned on H&E images and low-resolution spatial transcriptomics. It is designed to address three major challenges in histology-assisted super-resolution: isolating expression-relevant features from visually complex H&E images; achieving spatially precise multimodal alignment in diffusion-based frameworks; and modeling gene-specific variation across expression channels. The framework combines a conditional diffusion model with three modules—a semantic distillation network, a spatial alignment module, and a channel-aware adversarial learner—to enhance spatial fidelity and gene-level coherence in high-resolution spatial transcriptomics predictions (Liu et al., 10 Aug 2025).

1. Problem setting and conceptual scope

Spatial transcriptomics reveals spatial heterogeneity of gene expression, yet its resolution is limited by current platforms. Recent methods enhance resolution via H&E-stained histology, but the central difficulty is not only spatial upsampling; it is also the extraction of expression-relevant morphology, the alignment of histology with transcriptomic measurements under severe resolution mismatch, and the preservation of gene-specific spatial structure.

HaDM-ST models the conditional distribution of high-resolution spatial transcriptomics maps given H&E images and low-resolution spatial transcriptomics measurements. In the notation used for the framework,

$$\tilde{\mathbf{s}} \in \mathbb{R}^{C \times H_l \times W_l}$$

denotes the low-resolution ST tensor with $C$ genes over $H_l \times W_l$ spots,

$$\mathbf{m} \in \mathbb{R}^{3 \times H_m \times W_m}$$

denotes the H&E image with $H_m \approx 10 H_l$ and $W_m \approx 10 W_l$, and

$$\hat{\mathbf{s}} \in \mathbb{R}^{C \times H \times W}$$

denotes the output high-resolution ST map.

The framework is therefore not a histology-only image translation system. A common simplification is to describe this class of models as H&E-to-expression regression. HaDM-ST instead conditions jointly on H&E images and low-resolution ST, and its architecture is organized around explicit multimodal correspondence and gene-wise modeling rather than simple fusion.

2. Conditional diffusion backbone

The backbone of HaDM-ST is a conditional diffusion model. The clean high-resolution ST sample $\mathbf{s}_0$ is progressively corrupted through a forward degradation process formulated as in Denoising Diffusion Probabilistic Models (Ho et al., 2020): $$q(\mathbf{s}_{1:T}\mid\mathbf{s}_0) = \prod_{t=1}^T q(\mathbf{s}_t\mid\mathbf{s}_{t-1}), \qquad q(\mathbf{s}_t\mid\mathbf{s}_{t-1}) = \mathcal{N}\bigl(\mathbf{s}_t; \sqrt{1-\beta_t}\,\mathbf{s}_{t-1}, \beta_t \mathbf{I}\bigr).$$ The stepwise noising is controlled by a variance schedule $\{\beta_t\}$.

In the reverse process, denoising is conditioned on fused histology and low-resolution transcriptomic features. At each timestep $C$0, the conditioning vector is written as

$C$1

and the reverse transition is

$C$2

The mean is parameterized as in DDPM using a U-Net with noise prediction head $C$3.

This formulation places HaDM-ST within diffusion-based generative modeling, but the paper’s emphasis is on how the conditioning signal is constructed. The architectural novelty is concentrated in the modules that define what information from H&E and low-resolution ST enters the reverse denoising trajectory.

3. Histology-driven semantic distillation and cross-modal alignment

The first module is the H&E-Driven Semantic Distillation (HSD) Module. Its stated purpose is to address the fact that H&E images encode rich but noisy morphology, and only some patterns are causally linked to gene expression. The module takes as input the raw H&E image $C$4 and its segmentation map $C$5, and uses a transformer $C$6 to distill high-level semantic features: $C$7 Cancer type descriptions are embedded via a pretrained BERT,

$C$8

and fused with the morphological features to inject global biological context. In the formulation provided, this fusion suppresses irrelevant visual signals and focuses on expression-relevant morphology (Liu et al., 10 Aug 2025).

The second module is Cross-Modal Spatial Alignment (CMSA), which addresses the difficulty of pixel-level spatial alignment under both resolution mismatch and biological differences between H&E and low-resolution ST. Features $C$9 and $H_l \times W_l$0 are extracted from H&E and low-resolution ST, respectively, and compared through cosine similarity and Euclidean distance: $H_l \times W_l$1 Top $H_l \times W_l$2 of region pairs by cosine similarity are treated as positives, and bottom $H_l \times W_l$3 as negatives. The spatial alignment loss is multi-component: $H_l \times W_l$4 Here, $H_l \times W_l$5 maximizes mutual information between aligned features, while $H_l \times W_l$6 and $H_l \times W_l$7 enforce distance structure between positives and negatives.

Taken together, HSD and CMSA define the histology-to-transcriptomics interface. HSD filters histological content toward predictive cues, whereas CMSA enforces fine-grained, region-to-region spatial alignment across modalities. This division of labor is central to the framework’s attempt to improve both spatial precision and semantic relevance.

4. Gene-wise differential adversarial learning

The third module is Gene-wise Differential Adversarial Learning (GDAL). Its motivation is that real ST data exhibits complex, gene-specific spatial patterns and gene–gene correlation, whereas prior approaches often treat all genes globally and can miss channel-specific nuances.

GDAL constructs a co-expression graph $H_l \times W_l$8 in which each gene channel $H_l \times W_l$9 is a node and edge weights reflect gene expression correlations. A graph neural network then updates node representations according to

$$\mathbf{m} \in \mathbb{R}^{3 \times H_m \times W_m}$$0

where $$\mathbf{m} \in \mathbb{R}^{3 \times H_m \times W_m}$$1 is a learnable, attention-based edge weight. The resulting embeddings are fed to a channel-aware adversarial discriminator that distinguishes real from generated high-resolution ST at the gene or channel level (Liu et al., 10 Aug 2025).

This adversarial design is explicitly relational rather than independent across channels. The module does not merely supervise each gene separately; it also encodes inter-gene relationships during adversarial learning. The intended effect is to drive the generator toward gene-specific and biologically plausible spatial patterns.

The training objectives listed for the full system are the standard denoising score matching objective for the diffusion model, the contrastive loss for CMSA, and the adversarial loss associated with the GNN-based discriminator. The paper’s framing therefore couples generative denoising, multimodal alignment, and channel-aware discrimination within a single high-resolution ST generation pipeline.

5. Empirical setting and reported performance

The reported experiments use two Xenium public spatial transcriptomics cohorts: Mouse Brain and Human Breast. The evaluation covers 200 highly variable genes, with 514 slides and 61,680 tiles in total. The reported metrics are SSIM (Structural Similarity Index Measure), which evaluates local structural similarity, and RMSE (Root Mean Square Error), which measures pixel-wise prediction error (Liu et al., 10 Aug 2025).

Tissue	Approach	RMSE / SSIM
Mouse Brain	TESLA	0.2489 / 0.1373
Mouse Brain	iStar	0.3088 / 0.0995
Mouse Brain	HSG	0.2000 / 0.2648
Mouse Brain	Ours	0.1630 / 0.3184
Human Breast	TESLA	0.3302 / 0.0655
Human Breast	iStar	0.3071 / 0.0486
Human Breast	HSG	0.2832 / 0.0533
Human Breast	Ours	0.2304 / 0.4663

The reported gains are expressed as follows. SSIM increases by at least +0.0370 on mouse brain and +0.4008 on human breast over the best baselines, while RMSE decreases by at least -0.053 on mouse and -0.0528 on breast. The qualitative description accompanying these results states that visualizations show better alignment and gene expression boundaries.

Within the paper’s empirical scope, these results are presented as evidence that the combined effect of semantic distillation, spatial alignment, and channel-aware adversarial learning improves both structural agreement and gene-level coherence in high-resolution ST prediction.

6. Relation to prior methods and interpretive context

HaDM-ST is positioned against methods such as TESLA, HiStoGene (HSG), and iStar, as well as conditional diffusion approaches such as ControlNet and Uni-ControlNet. The comparison drawn is specific: TESLA, HiStoGene, and iStar either operate at spot resolution, use simple concatenation or fusion, or lack explicit modeling of gene–gene correlation and pixel-to-pixel alignment. ControlNet and Uni-ControlNet are cited as conditional diffusion models for histology, but with simple fusion rather than the fine-grained alignment described for CMSA (Liu et al., 10 Aug 2025).

This comparison is useful for clarifying several common misconceptions. One misconception is that multimodal conditioning in this setting can be reduced to naive channel concatenation. HaDM-ST is explicitly organized around contrastive, region-to-region spatial alignment across modalities. A second misconception is that supervision at the aggregate image level is sufficient for realistic ST generation. The framework instead emphasizes channel-aware, graph-based discrimination to capture gene-specific variation and inter-gene relationships.

The broader significance claimed for the method is that, by robustly aligning H&E histology with transcriptomic readouts and modeling gene-specific variation, it supports biologically meaningful super-resolution of gene expression. A plausible implication is that the method is particularly relevant where high-resolution spatial transcriptomics data are scarce or expensive to generate. Within that framing, HaDM-ST can be understood as a diffusion-based multimodal generator in which histological semantics, cross-modal co-registration, and gene-level relational structure are treated as separate but coupled modeling problems.