The computational description of chemical reactivity can become extremely complex when multiple different reaction products and intermediates come into play, forming a chemical reaction network. Therefore, computational methods for the automated construction of chemical reaction networks have been developed in the last decades. One of these methods, ab initio nanoreactor molecular dynamics (NMD), is based on external forces enhancing reactivity by e.g., periodically compressing the system and allowing it to relax. However, during the relaxation process, a significant simulation time is required to allow energy to dissipate and molecules to diffuse, making this part of the NMD simulation computationally intensive. This work aims to improve NMD by accelerating the diffusion process in the relaxation phase. We systematically investigate the speedup of reaction discovery gained by diffusion acceleration, leading to a factor of up to 28 in discovery frequency. Diffusion-accelerated nanoreactor molecular dynamics (DA-NMD) is then used to construct a reaction network of hydrogen sulfide oxidation under atmospheric conditions, where reactions are automatically detected by a change in the bond order and bond distance. A reaction network of 108 molecular species and 399 elementary reactions was constructed starting from hydrogen sulfide, hydroxy radicals, and molecular oxygen covering a broad variety of sulfur-oxygen chemistry and oxidation states of the sulfur atom ranging from -II to +VI.