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In real-world advertising systems, conversions have different types in nature and ads can be shown in different display scenarios, both of which highly impact the actual conversion rate (CVR). This results in the multi-type and multi-scenario CVR prediction problem. A desired model for this problem should satisfy the following requirements: 1) Accuracy: the model should achieve fine-grained accuracy with respect to any conversion type in any display scenario. 2) Scalability: the model parameter size should be affordable. 3) Convenience: the model should not require a large amount of effort in data partitioning, subset processing and separate storage. Existing approaches cannot simultaneously satisfy these requirements. For example, building a separate model for each (conversion type, display scenario) pair is neither scalable nor convenient. Building a unified model trained on all the data with conversion type and display scenario included as two features is not accurate enough. In this paper, we propose the Masked Multi-domain Network (MMN) to solve this problem. To achieve the accuracy requirement, we model domain-specific parameters and propose a dynamically weighted loss to account for the loss scale imbalance issue within each mini-batch. To achieve the scalability requirement, we propose a parameter sharing and composition strategy to reduce model parameters from a product space to a sum space. To achieve the convenience requirement, we propose an auto-masking strategy which can take mixed data from all the domains as input. It avoids the overhead caused by data partitioning, individual processing and separate storage. Both offline and online experimental results validate the superiority of MMN for multi-type and multi-scenario CVR prediction. MMN is now the serving model for real-time CVR prediction in UC Toutiao., Comment: CIKM 2023 (larger figures)