In real applications, one object (e.g., image) can be described by multiple instances (e.g., image patches) and simultaneously associated with multiple labels. Such applications can be formulated as multi-instance multi-label learning (MIML) problems and have been extensively studied currently. Existing MIML methods are useful in many applications but most of which suffer from relatively low accuracy and training efficiency due to: i) the inter-label correlations are neglected; ii) the inter-instance correlations cannot be learned directly with other types of correlations due to the missing instance labels; iii) diverse inter-correlations (e.g., inter-label correlations, inter-instance correlations) can only be learned in multiple stages. To resolve these issues, a new single-stage framework called broad multi-instance multi-label learning (BMIML) is proposed. In BMIML, there are three innovative modules: i) auto-weighted label enhancement learning (AWLEL) based on broad learning system (BLS) is designed, which simultaneously captures the inter-label correlations while traditional BLS cannot; ii) A specific MIML neural network, scalable multi-instance probabilistic regression (SMIPR) is constructed to effectively estimate the inter-instance correlations, which can provide additional probabilistic information for learning; iii) Finally, an interactive decision optimization (IDO) is designed to combine and optimize the results from AWLEL and SMIPR and form a single-stage framework. Consequently, BMIML can achieve simultaneous learning of diverse inter-correlations between whole images, instances, and labels in single stage for higher classification accuracy and much faster training time. Experiments show that BMIML is highly competitive to (or even better than) existing methods in accuracy and much faster.