Scalable Generation of Spatial Transcriptomics from Histology Images via Whole-Slide Flow Matching

We sincerely thank you for the insightful comments and will revise the manuscript accordingly. Please see our detailed responses below:

A complex system with several modules and hyperparameters makes it challenging to evaluate.

Ans: Thank you so much for the feedback. STFlow primarily consists of two core components: (1) a frame averaging (FA)-based encoder and (2) a flow matching (FM) optimization framework. We evaluate their effectiveness by (i) comparing different geometric encoders and ablating FA, and (ii) removing the iterative refinement process. Additionally, we provide results on varying the number of refinement steps and ZINB prior hyperparameters to further assess stability below. We will refine our discussion to more clearly highlight each component’s contribution.

We greatly appreciate your valuable suggestions and will revise the manuscript accordingly. Due to character limits, all additional results are available in our anonymous codebase: https://anonymous.4open.science/r/Anonymous_STFlow-3616/.

I found it quite difficult to follow and understand the method description in Section 3.3

Ans: We apologize for the confusion. Section 3.3 introduces the formulation of frame averaging, which may be difficult to follow due to dense notation. We will simplify the notations and streamline the equations to better highlight the core idea and improve clarity for readers.

It would be interesting to see the computational cost for STFlow and UNI reported in Table 1.

Ans: We present the average inference time on the test set of each dataset across splits in link. The time required for visual feature extraction is excluded, as this step can be performed during preprocessing. Notably, STFlow demonstrates high efficiency due to its use of local neighborhood information.

Section 4.1, *"Additionally, some ST-based approaches fail to predict significantly correlated gene expression"*: Could you clarify exactly what you refer to in Table 1 here?

Ans: Yes, this refers to STNet (0.286) and HisToGene (0.237), which underperform compared to the pathology foundation model UNI (0.344) on HEST-1k. This highlights the advantage of using a foundation model and the need for an effective spatial encoder—HisToGene encodes spatial context but still underperforms. We will clarify this in the revised manuscript.

In Section 4.2, could perhaps clarify that these 3 datasets are from HEST-1k?

Ans: We apologize for any confusion and will clarify it in our manuscript: “We utilize two datasets from HEST and report the average correlation for each gene across different cross-validation folds. Specifically, the IDC dataset is used for GATA3 and ERBB2, while LUNG is used for UBE2C, and SKCM for VWF.”

It's not entirely clear to me what "STFlow w/o FM" in Table 2, Figure 4 and Table 4 means, does this correspond to setting S = 1 in Algorithm 2?

Ans: "STFlow w/o FM" refers to the model where the iterative refinement is removed and one-step prediction is performed, i.e., setting the number of sampling steps S = 1. We will clarify this in the revised manuscript to avoid confusion.

Figure 4 is neat, it would be interesting to see more examples like these, could you perhaps add a couple to the appendix?

Ans: We include two biomarker examples on a sample from the IDC dataset in link, which will be added to our manuscript.

It would also be interesting to see Figure 4-like visualizations of the predicted gene-expression during the iterative refinement process?

Ans: We include two examples showing how STFlow refines gene expression predictions in link. Step 1 shows the initial random sample Y_0, and Steps 2–5 indicate progressive denoising. The results illustrate how flow matching gradually converges to the final prediction via interpolation with a decay coefficient. The results will be included in the revised manuscript.

It would also be interesting to see the regression accuracy as a function of the number of refinement steps S.

Ans: We report STFlow’s performance across different numbers of refinement steps in link. The results show a clear improvement from one-step prediction (S=1) to introducing iterative refinement (S=2). In some datasets, performance improves up to S = 5 (e.g., PAAD: 0.488 → 0.507). However, gains plateau or slightly decline beyond that. This trend aligns with prior works like AlphaFlow and RNAFlow, which adopt S=5 as default. The analysis will be included in the revised manuscript.

Regarding the Limitations paragraph in Section 5: I think it would be relevant to refer to the results in Table 9 in the appendix here, or at least somewhere in the main paper? Because, I think these are encouraging results?

Ans: Yes, the model is generally robust to the choice of prior, as the iterative refinement process helps mitigate noise from the initialization. But the ZINB distribution introduces three additional hyperparameters that can impact the performance on certain datasets, such as 0.496~0.507 on PAAD as shown in link. Automatically estimating these parameters could be a valuable future direction.

Minor things regarding the writing.

Ans: We sincerely appreciate these helpful comments and will incorporate all the suggestions in the revised manuscript.

We sincerely thank you for the insightful comments and will revise the manuscript accordingly. Due to character limits, all additional results are available in our anonymous codebase: https://anonymous.4open.science/r/Anonymous_STFlow-3616/.

The Introduction analyzes the issues of existing schemes yet does not clearly explain how this work tackles these issues.

Ans: STFlow addresses the issues as follows: (1) it reduces computational complexity via a spatial local attention mechanism, (2) it enhances spatial dependency modeling by encoding and incorporating relative orientation into attention, and (3) it captures cell-cell interactions through flow matching that effectively uses gene expression as context. We will clarify these points in the manuscript.

The layout of some Tabs and Figs could be improved, *e.g.*, Tab 2 on page 6.

Ans: Thank you for pointing this out! We will improve the layout of all tables and figures in the revised manuscript.

Could the authors provide the visualization of the inference process of FM. This experiments could help readers better understand STFlow.

Ans: We include two examples showing how STFlow refines gene expression predictions in link. Step 1 shows the initial random sample Y_0, and Steps 2–5 indicate progressive denoising. The results illustrate how flow matching gradually converges to the final prediction via interpolation with a decay coefficient. The results will be included in the revised manuscript.

Could the authors represent the results of STFlow with different S.

Ans: We report STFlow’s performance across different numbers of refinement steps in link. The results show a clear improvement from one-step prediction (S=1) to introducing iterative refinement (S=2). In certain datasets, performance improves up to S = 5 (e.g., PAAD: 0.488 → 0.507). However, gains plateau or slightly decline beyond that. This observation aligns with prior works such as AlphaFlow and RNAFlow, which adopt S=5 as the default setting. The analysis will be included in the revised manuscript.

Some results have large variance (Table 1).

Ans: For the HEST benchmark with cross-validation, the variances are generally low, indicating stable performance. On STImage, which uses a train-val-test split, slide-based methods show higher variance than spot-based ones, likely due to variability in spatial patterns and the noise introduced by slide-level aggregation. Nevertheless, STFlow achieves lower variance than the SOTA baseline TRIPLEX in most cases.

Some commonly-used metrics seem missing.

Ans: We followed the HEST-1k benchmark setup, which uses Pearson correlation to evaluate performance. Metrics like MSE or MAE depend on absolute expression values and can be influenced by different normalization strategies, making direct comparisons less reliable. The MSE metrics on HEST are shown in link, from which STFlow achieves the best performance.

How is the w/o FM implemented?

Ans: "STFlow w/o FM" refers to the model where the iterative refinement is removed and one-step prediction is performed, i.e., setting the number of sampling steps S = 1. We will clarify this in the revised manuscript to avoid confusion.

The effectiveness of one core design, *i.e.*, modeling the joint distribution p(Y0,⋯,YN|I0,⋯,IN), seems to lack convincing evidence.

Ans: Modeling the joint distribution captures dependencies across spatial spots, rather than predicting each independently. Our flow matching framework enables this by using whole-slide gene expressions as context during iterative refinement. Its effectiveness is shown in the “STFlow w/o FM” ablation, where removing the refinement process reduces the model to a one-step predictor. Prior gene imputation studies also support the value of leveraging spatial gene expression context.

It would be better to provide an intuitive explanation for how FM realizes the modeling of joint distribution.

Ans: Flow matching models the joint distribution by iteratively refining each spot’s gene expression using predictions from neighboring spots. This allows information to flow across spatial locations, so each prediction is influenced by its context. Through this process, the model learns how gene expressions co-vary across the tissue, effectively capturing the joint distribution.

In Algo.2, is Y0 sampled once or multiple times when deriving the prediction of one WSI from the model?

Ans: In our current implementation, Y_0 is sampled once per inference. A potential improvement is to sample multiple times and select the most confident prediction using a confidence model, which will be explored for future work.

Thanks for your feedback on our work! We will explain your concerns point by point.

The authors should perform a hyperparameter study on the number of refinement steps in the flow matching process.

Ans: We report STFlow’s performance across different numbers of refinement steps below. The results show a clear improvement from one-step prediction (S=1) to introducing iterative refinement (S=2). In some datasets, performance continues to improve up to S = 5 (e.g., PAAD: 0.488 → 0.507). However, gains plateau or slightly decline beyond that. This trend aligns with prior works like AlphaFlow and RNAFlow, which also adopt S=5 as default. The analysis will be included in the revised manuscript.

The authors should conduct an ablation study on the hyperparameters of the ZINB prior (μ, ϕ, π) to demonstrate their impact on prediction performance.

Ans: We set the zero-inflation probability $\pi=0.5$, as higher dropout rates degrade ZINB to a near-zero distribution. We conducted an ablation over the mean $\mu\in\{0.1,0.2,0.4\}$ and dispersion $\phi\in\{1,2,4\}$, with results shown below. STFlow is generally robust to these hyperparameters due to its iterative refinement, though performance can vary slightly on some datasets (e.g., 0.496–0.507 on PAAD). Exploring automated strategies for tuning prior parameters is a promising direction, as noted in our Limitation section.