SIDE-real is the first fully simulation-based hierarchical analysis of the light curves of a population of low-redshift SNæ Ia. It relies on a hardware-accelerated and parallelisable Bayesian forward model (simulator) that includes stochastic variations in each SN’s spectral flux, probabilistic extinction from dust in the host and in the Milky Way, the effects of redshift and distance, and realistic instrumental noise. The simulator’s output is used to train a bespoke neural network (dubbed a Super Tuple) that directly ingests the uncompressed collection of light curves, thus circumventing the expensive individual-object fitting stage present in all current studies. This allows for efficient complete hierarchical inference of the SN Ia absolute magnitudes and host-galaxy dust properties, both at the population level and of the parameters of the individual objects, as well as obtaining coverage guarantees for the results through Bayesian validation and frequentist calibration enabled by inference amortisation. We apply this framework to both simulated and real optical and near infrared light curves of 86 SNæ Ia from the Carnegie Supernova Project, deriving marginal posteriors in excellent agreement with previous work and traditional likelihood-based methods.