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Diffuse interstellar bands (DIBs) are broad absorption features associatedwith interstellar dust and can serve as chemical and kinematic tracers.Conventional measurements of DIBs in stellar spectra are complicated byresiduals between observations and best-fit stellar models. To overcome this,we simultaneously model the spectrum as a combination of stellar, dust, andresidual components, with full posteriors on the joint distribution of thecomponents. This decomposition is obtained by modeling each component as a drawfrom a high-dimensional Gaussian distribution in the data-space (the observedspectrum) -- a method we call "Marginalized Analytic Data-space GaussianInference for Component Separation" (MADGICS). We use a data-driven prior forthe stellar component, which avoids missing stellar features not well-modeledby synthetic spectra. This technique provides statistically rigorousuncertainties and detection thresholds, which are required to work in the lowsignal-to-noise regime that is commonplace for dusty lines of sight. Wereprocess all public Gaia DR3 RVS spectra and present an improved 8621 \r{A}DIB catalog, free of detectable stellar line contamination. We constrain therest-frame wavelength to $8623.14 \pm 0.087$ \r{A} (vacuum), find nosignificant evidence for DIBs in the Local Bubble from the $1/6^{\rm{th}}$ ofRVS spectra that are public, and show unprecedented correlation with kinematicsubstructure in Galactic CO maps. We validate the catalog, its reporteduncertainties, and biases using synthetic injection tests. We believe MADGICSprovides a viable path forward for large-scale spectral line measurements inthe presence of complex spectral contamination.

Measuring the 8621 \r{A} Diffuse Interstellar Band in Gaia DR3 RVS Spectra: Obtaining a Clean Catalog by Marginalizing over Stellar Types