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Models of stellar population synthesis (SPS) are the fundamental tool that relates the physical properties of a galaxy to its spectral energy distribution (SED). In this paper, we present DSPS: a python package for SPS. All of the functionality in DSPS is implemented natively in the JAX library for automatic differentiation, and so our predictions for galaxy photometry are fully differentiable, and directly inherit the performance benefits of JAX, including portability onto GPUs. DSPS also implements several novel features, such as i) a flexible empirical model for stellar metallicity that incorporates correlations with stellar age, ii) support for the Diffstar model that provides a physically-motivated connection between the star formation history of a galaxy (SFH) and the mass assembly of its underlying dark matter halo. We detail a set of theoretical techniques for using autodiff to calculate gradients of predictions for galaxy SEDs with respect to SPS parameters that control a range of physical effects, including SFH, stellar metallicity, nebular emission, and dust attenuation. When forward modelling the colours of a synthetic galaxy population, we find that DSPS can provide a factor of 5 speed-up over standard SPS codes on a CPU, and a factor of 300-400 on a modern GPU. When coupled with gradient-based techniques for optimization and inference, DSPS makes it practical to conduct expansive likelihood analyses of simulation-based models of the galaxy–halo connection that fully forward model galaxy spectra and photometry.

We present Diffstar , a smooth parametric model for the in situ star formation history (SFH) of galaxies. The Diffstar model is distinct from traditional SFH models because it is parametrized directly in terms of basic features of galaxy formation physics. Diffstar includes ingredients for: the halo mass assembly history; the accretion of gas into the dark matter halo; the fraction of gas that is eventually transformed into stars, ϵms; the time-scale over which this transformation occurs, τcons; and the possibility that some galaxies will experience a quenching event at time tq, and may subsequently experience rejuvenated star formation. We show that our model is sufficiently flexible to describe the average stellar mass histories of galaxies in both the IllustrisTNG (TNG) and UniverseMachine (UM) simulations with an accuracy of ∼0.1 dex across most of cosmic time. We use Diffstar to compare TNG to UM in common physical terms, finding that: (i) star formation in UM is less efficient and burstier relative to TNG; (ii) UM galaxies have longer gas consumption time-scales, relative to TNG; (iii) rejuvenated star formation is ubiquitous in UM, whereas quenched TNG galaxies rarely experience sustained rejuvenation; and (iv) in both simulations, the distributions of ϵms, τcons, and tq share a common characteristic dependence upon halo mass, and present significant correlations with halo assembly history. We conclude with a discussion of how Diffstar can be used in future applications to fit the SEDs of individual observed galaxies, as well as in forward-modelling applications that populate cosmological simulations with synthetic galaxies.