SnapATAC2 is a fast, scalable, and versatile tool for analyzing single-cell omics data. It introduces a nonlinear dimensionality reduction algorithm that efficiently captures the heterogeneity of single-cell data while maintaining computational efficiency and memory usage, scaling linearly with the number of cells. The algorithm is implemented in the Python package SnapATAC2, which offers improved performance, reduced memory usage, and a comprehensive analysis framework for diverse single-cell omics data. The key innovation of SnapATAC2 is its matrix-free spectral embedding algorithm, which projects single-cell data into a low-dimensional space without constructing a full similarity matrix, significantly reducing computational time and memory requirements. This approach allows for efficient processing of large-scale datasets and is applicable to various single-cell omics data types, including scATAC-seq, scRNA-seq, scHi-C, and single-cell DNA methylation data. SnapATAC2 demonstrates exceptional performance in terms of speed, scalability, and precision in resolving cell heterogeneity. It is also robust to noise and varying sequencing depths, outperforming other methods in clustering accuracy and bio-conservation scores. The package is designed to be flexible and scalable, supporting a wide range of single-cell data types and integrating with other software tools in the single-cell analytics ecosystem. SnapATAC2 is also applicable to multi-omics data, enabling joint embedding of multiple data views for comprehensive analysis. The algorithm is efficient and scalable, making it a powerful tool for researchers studying gene regulatory programs in complex tissues.SnapATAC2 is a fast, scalable, and versatile tool for analyzing single-cell omics data. It introduces a nonlinear dimensionality reduction algorithm that efficiently captures the heterogeneity of single-cell data while maintaining computational efficiency and memory usage, scaling linearly with the number of cells. The algorithm is implemented in the Python package SnapATAC2, which offers improved performance, reduced memory usage, and a comprehensive analysis framework for diverse single-cell omics data. The key innovation of SnapATAC2 is its matrix-free spectral embedding algorithm, which projects single-cell data into a low-dimensional space without constructing a full similarity matrix, significantly reducing computational time and memory requirements. This approach allows for efficient processing of large-scale datasets and is applicable to various single-cell omics data types, including scATAC-seq, scRNA-seq, scHi-C, and single-cell DNA methylation data. SnapATAC2 demonstrates exceptional performance in terms of speed, scalability, and precision in resolving cell heterogeneity. It is also robust to noise and varying sequencing depths, outperforming other methods in clustering accuracy and bio-conservation scores. The package is designed to be flexible and scalable, supporting a wide range of single-cell data types and integrating with other software tools in the single-cell analytics ecosystem. SnapATAC2 is also applicable to multi-omics data, enabling joint embedding of multiple data views for comprehensive analysis. The algorithm is efficient and scalable, making it a powerful tool for researchers studying gene regulatory programs in complex tissues.