Research on learned cardinality estimation has achieved significant progress in recent years. However, existing methods still face distinct challenges that hinder their practical deployment in production environments. We conceptualize these challenges as the "Trilemma of Cardinality Estimation", where learned cardinality estimation methods struggle to balance generality, accuracy, and updatability. To address these challenges, we introduce DistJoin, a join cardinality estimator based on efficient distribution prediction using multi-autoregressive models. Our contributions are threefold: (1) We propose a method for estimating both equi and non-equi join cardinality by leveraging the conditional probability distributions of individual tables in a decoupled manner. (2) To meet the requirements of efficient training and inference for DistJoin, we develop Adaptive Neural Predicate Modulation (ANPM), a high-throughput conditional probability distribution estimation model. (3) We formally analyze the variance of existing similar methods and demonstrate that such approaches suffer from variance accumulation issues. To mitigate this problem, DistJoin employs a selectivity-based approach rather than a count-based approach to infer join cardinality, effectively reducing variance. In summary, DistJoin not only represents the first data-driven method to effectively support both equi and non-equi joins but also demonstrates superior accuracy while enabling fast and flexible updates. We evaluate DistJoin on JOB-light and JOB-light-ranges, extending the evaluation to non-equi join conditions. The results demonstrate that our approach achieves the highest accuracy, robustness to data updates, generality, and comparable update and inference speed relative to existing methods.