We originally report the use of a neural network-based method for diagnosing multiple key parameters in axis-symmetric laminar sooting flames. A Bayesian optimized back propagation neural network (BPNN) is developed and applied to flame luminosity to predict the planar distribution of soot volume fraction, temperature, and primary particle diameter. The feasibility and robustness of this approach are firstly assessed using numerical modeling results and then further validated with experimental results of a series of laminar diffusion sooting flames. This proposed BPNN model-based flame luminosity approach shows high prediction accuracies, typically up to 114 K, 0.25 ppm, and 2.56 nm for soot temperature, volume fraction, and primary particle diameter, respectively. We believe that the present machine learning-assisted optical diagnostics paves a more efficient, lower costing, and high-fidelity way for multi-parameters simultaneous diagnosis in combustion and reacting flows.