Streaming generation models are increasingly utilized across various fields, with the Transducer architecture being particularly popular in industrial applications. However, its input-synchronous decoding mechanism presents challenges in tasks requiring non-monotonic alignments, such as simultaneous translation, leading to suboptimal performance in these contexts. In this research, we address this issue by tightly integrating Transducer's decoding with the history of input stream via a learnable monotonic attention mechanism. Our approach leverages the forwardbackward algorithm to infer the posterior probability of alignments between the predictor states and input timestamps, which is then used to estimate the context representations of monotonic attention in training. This allows Transducer models to adaptively adjust the scope of attention based on their predictions, avoiding the need to enumerate the exponentially large alignment space. Extensive experiments demonstrate that our MonoAttn-Transducer significantly enhances the handling of non-monotonic alignments in streaming generation, offering a robust solution for Transducer-based frameworks to tackle more complex streaming generation tasks. Unlike modern turn-based large language models, streaming models need to start generating the output before the input is completely read. Popular streaming generation methods can be broadly divided into two categories: Attentionbased Encoder-Decoder (AED; Bahdanau et al., 2015) and Transducer (Graves, 2012). Streaming AED models adapt the conventional sequence-to-sequence framework (Bahdanau, 2014) to support streaming generation. They often rely on an external policy module to determine the READ/WRITE actions in inference and to direct the scope of cross-attention in training. Examples include Wait-k policy (Ma et al., 2019) and monotonic attention-based methods (Raffel et al., 2017; Arivazhagan et al., 2019; Ma et al., 2020d; 2023a).