Binary Decision Diagrams (BDDs) are instrumental in many electronic design automation (EDA) tasks thanks to their compact representation of Boolean functions. In BDD-based reversible-circuit synthesis, which is critical for quantum computing, the chosen variable ordering governs the number of BDD nodes and thus the key metrics of resource consumption, such as Quantum Cost. Because finding an optimal variable ordering for BDDs is an NP-complete problem, existing heuristics often degrade as circuit complexity grows. We introduce BDD2Seq, a graph-to-sequence framework that couples a Graph Neural Network encoder with a Pointer-Network decoder and Diverse Beam Search to predict high-quality orderings. By treating the circuit netlist as a graph, BDD2Seq learns structural dependencies that conventional heuristics overlooked, yielding smaller BDDs and faster synthesis. Extensive experiments on three public benchmarks show that BDD2Seq achieves around 1.4 times lower Quantum Cost and 3.7 times faster synthesis than modern heuristic algorithms. To the best of our knowledge, this is the first work to tackle the variable-ordering problem in BDD-based reversible-circuit synthesis with a graph-based generative model and diversity-promoting decoding.

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