Event reconstruction is a central step in many particle physics experiments, turning detector observables into parameter estimates; for example estimating the energy of an interaction given the sensor readout of a detector. A corresponding likelihood function is often intractable, and approximations need to be constructed. In our work, we first show how the full likelihood for a many-sensor detector can be broken apart into smaller terms, and secondly how we can train neural networks to approximate all terms solely based on forward simulation. Our technique results in a fast, flexible, and close-to-optimal surrogate model proportional to the likelihood and can be used in conjunction with standard inference techniques. We illustrate our technique for parameter inference in neutrino telescopes based on maximum likelihood and Bayesian posterior sampling. Given its great flexibility, we also showcase our method for detector optimization, and apply it to simulation of a ton-scale water-based liquid scintillator detector. tests used to compare In the likelihood be used to evaluate posterior over desired parameters.