Automatically generating regular expressions (abbrev. regexes) from natural language description (NL2RE) has been an emerging research area. Prior studies treat regex as a linear sequence of tokens and generate the final expressions autoregressively in a single pass. They did not take into account the step-by-step internal text-matching processes behind the final results. This significantly hinders the efficacy and interpretability of regex generation by neural language models. In this paper, we propose a new paradigm called InfeRE, which decomposes the generation of regexes into chains of step-bystep inference. To enhance the robustness, we introduce a self-consistency decoding mechanism that ensembles multiple outputs sampled from different models. We evaluate InfeRE on two publicly available datasets, NL-RX-Turk and KB13, and compare the results with state-of-the-art approaches and the popular tree-based generation approach TRANX. Experimental results show that InfeRE substantially outperforms previous baselines, yielding 16.3% and 14.7% improvement in DFA@5 accuracy on two datasets, respectively.