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Conditional graphic layout generation, which generates realistic layouts according to user constraints, is a challenging task that has not been well-studied yet. First, there is limited discussion about how to handle diverse user constraints flexibly and uniformly. Second, to make the layouts conform to user constraints, existing work often sacrifices generation quality significantly. In this work, we propose LayoutFormer++ to tackle the above problems. First, to flexibly handle diverse constraints, we propose a constraint serialization scheme, which represents different user constraints as sequences of tokens with a predefined format. Then, we formulate conditional layout generation as a sequence-to-sequence transformation, and leverage encoder-decoder framework with Transformer as the basic architecture. Furthermore, to make the layout better meet user requirements without harming quality, we propose a decoding space restriction strategy. Specifically, we prune the predicted distribution by ignoring the options that definitely violate user constraints and likely result in low-quality layouts, and make the model samples from the restricted distribution. Experiments demonstrate that LayoutFormer++ outperforms existing approaches on all the tasks in terms of both better generation quality and less constraint violation.