Title: CaLFADS: latent factor analysis of dynamical systems in calcium imaging data. Abstract: Dynamic latent variable modelling has been a hugely powerful tool in understanding how spiking activity in populations of neurons can perform computations necessary for adaptive behaviour. The success of such approaches has been enabled by the ability to construct models derived with the characterization of spiking activity as point-processes since spiking dynamics occur on a much faster time-scale than the computational dynamics being inferred. Other experimental techniques, such as calcium imaging, pose a problem for latent variable modelling of computational dynamics, since the time-scales of calcium dynamics and computational dynamics overlap. As such, the success of dynamic latent variable modelling in calcium imaging data rests on being able to disentangle the contribution of these two sources of variation. Here we extend recent advances using variational autoencoders to analyze neural data, by incorporating a ladder architecture that can infer a hierarchy of dynamical systems. Using built-in inductive biases for calcium dynamics, we can capture calcium flux as well as underlying dynamics of neural computation. First, we demonstrate with synthetic calcium data that we can correctly infer an underlying Lorenz attractor at the same time as calcium dynamics. Next, we show that we can infer appropriate rotational dynamics in spiking data from macaque motor cortex after it has been converted into calcium fluorescence data via a calcium dynamics model. Finally, we show that our method applied to real calcium imaging data from primary visual cortex in mice allows us to infer latent factors that carry salient sensory information about unexpected stimuli. These results demonstrate that variational ladder autoencoders are a promising approach for inferring hierarchical dynamics in experimental settings where the measured variable has its own slow dynamics, such as calcium imaging data, thereby providing the neuroscience community with a new analysis tool for a wider array of data modalities.