The spectral energy distributions (SEDs) of galaxies offer detailed insights into their stellar populations, capturing key physical properties such as stellar mass, star formation history (SFH), metallicity, and dust attenuation. However, inferring these properties from SEDs is a highly degenerate inverse problem, particularly when using integrated observations across a limited range of photometric bands. We present an efficient Bayesian SED-fitting framework tailored to multiwavelength pixel photometry from the JWST Advanced Deep Extragalactic Survey (JADES). Our method employs simulation-based inference to enable rapid posterior sampling across galaxy pixels, leveraging the unprecedented spatial resolution, wavelength coverage, and depth provided by the survey. It is trained on synthetic photometry generated from MILES stellar population models, incorporating both parametric and non-parametric SFHs, realistic noise, and JADES-like filter sensitivity thresholds. We validated this amortised inference approach on mock datasets, achieving robust and well-calibrated posterior distributions, with an R2 score of 0.99 for stellar mass. Applying our pipeline to real observations, we derived spatially resolved maps of stellar population properties down to S/Npixel = 5 (averaged over F277W, F356W, and F444W) for 1083 JADES galaxies and ∼2 million pixels with spectroscopic redshifts. These maps enable the identification of dusty or starburst regions, offering insights into mass growth and structural assembly. We assessed the outshining phenomenon by comparing pixel-based and integrated stellar mass estimates, finding a limited impact only in low-mass galaxies (< 108 M⊙), but with systematic differences of ∼0.20 dex linked to SFH priors. With an average posterior sampling speed of 10−4 seconds per pixel and a total inference time of ∼1 CPU-day for the full dataset, our model offers a scalable solution for extracting high-fidelity stellar population properties from HST+JWST datasets, paving the way for statistical studies on sub-galactic scales.