Reduces 3-sulfolactaldehyde (SLA) to 2,3-dihydroxypropane 1-sulfonate (DHPS). (2S)-3-sulfopropanediol + NAD(+) = (2S)-3-sulfolactaldehyde + H(+) + NADH Belongs to the HIBADH-related family. 3-sulfolactaldehyde reductase subfamily.