Acute myeloid leukaemia (AML) is a haematological cancer in the bone marrow, with accumulation and expansion of immature cells of the myeloid lineage. Standard treatment of AML is chemotherapy, which does not achieve durable remission in most patients. Personalised medicine including immunotherapies have the potential to target chemotherapy resistant cells and achieve long-term remission. Identifying suitable targets for AML therapy is hampered by the heterogeneity and complex clonal composition of the cancer, as well as its complex evolution as the disease progresses. We aim to build a single-cell cytometry AML map to identify malignant cells and place them along the developmental trajectory using data from 20 patients and three time points over the course of the disease. We train a variational auto-encoder structure on healthy cells, which learns cellular reconstruction as well as the cell type classification. The latent space of the auto-encoder provides a meaningful representation of the healthy bone marrow cells to which we can map new cells. We use the trajectory assignment to segment patients into groups as well as to study the time evolution of the disease in terms of the distribution of malignant cells across the myeloid lineage.