Animals respond to dietary changes by adapting their metabolism to available nutrients through insulin and insulin-like growth factor signalling. Restricting calorie intake generally extends life and health span, but Drosophila fed non-ideal sugars such as galactose are stressed and have shorter life spans. Here, we report that although these flies have shorter life spans, their offspring show significant life extension if switched to a normal sugar (glucose) diet. We define this as TGH or trans-generational hormesis, a beneficial effect that comes from a mild stress. We trace the effects to changes in stress responses in parents, ROS production, effects on lipid metabolism, and changes in chromatin and gene expression. We find that this mechanism is similar to what happens to the long lived Indy mutants on normal food, but surprisingly find that Indy is required for life span extension for galactose fed flies. Indy mutant flies grown on galactose do not live longer as do their siblings grown on glucose, rather overexpression of Indy rescues lifespan for galactose reared flies. We define a process where sugar metabolism can generate epigenetic changes that are inherited by offspring, providing a mechanism for how transgenerational nutrient sensitivities are passed on.