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The memory demand of virtual machines (VMs) is increasing, while DRAM has limited capacity and high power consumption. Non-volatile memory (NVM) is an alternative to DRAM, but it has high latency and low bandwidth. We observe that the VM with heterogeneous memory may incur up to a $1.5\times$ slowdown compared to a DRAM VM, if not managed well. However, none of the state-of-the-art heterogeneous memory management designs are customized for virtualization on a real system. In this paper, we propose HMM-V, a Heterogeneous Memory Management system for Virtualization. HMM-V automatically determines page hotness and migrates pages between DRAM and NVM to achieve performance close to the DRAM system. First, HMM-V tracks memory accesses through page table manipulation, but reduces the cost by leveraging Intel page-modification logging (PML) and a multi-level queue. Second, HMM-V quantifies the ``temperature'' of page and determines the hot set with bucket-sorting. HMM-V then efficiently migrates pages with minimal access pause and handles dirty pages with the assistance of PML. Finally, HMM-V provides pooling management to balance precious DRAM across multiple VMs to maximize utilization and overall performance. HMM-V is implemented on a real system with Intel Optane DC persistent memory. The four-VM co-running results show that HMM-V outperforms NUMA balancing and hardware management (Intel Optane memory mode) by $51\%$ and $31\%$, respectively.