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One key cellular strategy that enables these functions is stochastic gene expression programs. However, understanding how transcriptional bursting, and consequently, cell fate, responds to DNA damage on a genome-wide scale poses a challenge. In this study, we propose an interpretable and scalable inference framework, DeepTX, that leverages deep learning methods to connect mechanistic models and single-cell RNA sequencing (scRNA-seq) data, thereby revealing genome-wide transcriptional burst kinetics. This framework enables rapid and accurate solutions to transcription models and the inference of transcriptional burst kinetics from scRNA-seq data. Applying this framework to several scRNA-seq datasets of DNA-damaging drug treatments, we observed that fluctuations in transcriptional bursting induced by different drugs were associated with distinct fate decisions: 5\u2032-iodo-2\u2032-deoxyuridine treatment was associated with differentiation in mouse embryonic stem cells by increasing the burst size of gene expression, while low- and high-dose 5-fluorouracil treatments in human colon cancer cells were associated with changes in burst frequency that corresponded to apoptosis- and survival-related fate, respectively. 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