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Query optimizers rely on accurate cardinality estimation (CardEst) to produce good execution plans. The core problem of CardEst is how to model the rich joint distribution of attributes in an accurate and compact manner. Despite decades of research, existing methods either over simplify the models only using independent factorization which leads to inaccurate estimates, or over complicate them by lossless conditional factorization without any independent assumption which results in slow probability computation. In this paper, we propose FLAT, a CardEst method that is simultaneously fast in probability computation, lightweight in model size and accurate in estimation quality. The key idea of FLAT is a novel unsupervised graphical model, called FSPN. It utilizes both independent and conditional factorization to adaptively model different levels of attributes correlations, and thus dovetails their advantages. FLAT supports efficient online probability computation in near liner time on the underlying FSPN model, provides effective offline model construction and enables incremental model updates. It can estimate cardinality for both single table queries and multi table join queries. Extensive experimental study demonstrates the superiority of FLAT over existing CardEst methods on well known IMDB benchmarks: FLAT achieves 1 to 5 orders of magnitude better accuracy, 1 to 3 orders of magnitude faster probability computation speed and 1 to 2 orders of magnitude lower storage cost. We also integrate FLAT into Postgres to perform an end to end test. It improves the query execution time by 12.9% on the benchmark workload, which is very close to the optimal result 14.2% using the true cardinality.