# SpaLSTF: Diffusion-based generative model with BiLSTM and XCA-Transformer for spatial transcriptomics imputation

## TL;DR

SpaLSTF is a new method using a diffusion model and BiLSTM to improve gene expression data in spatial transcriptomics, outperforming existing approaches.

## Contribution

Introduces SpaLSTF, a novel diffusion-based model with BiLSTM and XCA-Transformer for spatial transcriptomics imputation.

## Key findings

- SpaLSTF outperforms seven state-of-the-art methods in gene expression imputation.
- The method excels in cell population identification and spatial structure preservation.
- A dual Markov process and KL divergence regularization enhance model performance.

## Abstract

Spatial transcriptomics (ST) technologies provide powerful tools for analyzing spatial distribution patterns of gene expression in tissue samples. However, they are limited by sparse gene detection and incomplete expression coverage. Several computational approaches based on reference scRNA-seq have been proposed to impute ST data and have achieved impressive results. However, these methods fail to fully explore latent temporal dependencies among cells and cannot accurately capture hidden gene-level regulatory mechanisms. To overcome those limitations, we propose SpaLSTF, a novel method for enhancing ST gene expression using a conditional diffusion model guided by scRNA-seq data. SpaLSTF captures gene expression relationships through a dual Markov process: one progressively perturbs scRNA-seq data with noise, while the other denoises it to reconstruct the original distribution. To effectively model contextual dependencies among cell states, we adopt a bidirectional long short-term memory (BiLSTM) network. Furthermore, we design a cross-covariance attention mechanism within a Transformer (XCA-Transformer) to efficiently compute attention coefficients between gene expression and accurately predict the noise added at each step. In addition, we introduce a variational lower bound (VLB) objective and introduce Kullback-Leibler (KL) divergence as a regularization term, along with mean squared error loss, to ensure that the generated noise follows the target distribution. We compared the performance of SpaLSTF with seven state-of-the-art methods on twelve cross-platform datasets covering a variety of tissues and organs using nine evaluation metrics. Experimental results demonstrated that SpaLSTF outperforms competing methods in gene expression imputation, cell population identification, and spatial structure preservation.

Computational approaches based on reference scRNA-seq have been proposed to impute ST data and have some limitations. We propose SpaLSTF, a novel method for enhancing ST gene expression using a conditional diffusion model guided by scRNA-seq data. SpaLSTF captures gene expression relationships through a dual Markov process. We adopt a bidirectional long short-term memory (BiLSTM) network to effectively model contextual dependencies among cell states. Furthermore, we design a cross-covariance attention mechanism within a Transformer (XCA-Transformer) to efficiently compute attention coefficients between gene expression and accurately predict the noise added at each step. In addition, we adopt a variational lower bound (VLB) objective and introduce Kullback-Leibler (KL) divergence as a regularization term, along with mean squared error loss, to ensure that the generated noise follows the target distribution. Experimental results demonstrated that SpaLSTF outperforms competing methods in gene expression imputation, cell population identification, and spatial structure preservation.