Noise is a fundamental problem for information processing in neural systems. In decision-making, noise is thought to cause stochastic errors in choice. However, little is known about how noise arising from different sources may contribute differently to value coding and choice behaviors. Here, we examine how noise arising early versus late in the decision process differentially impacts context-dependent choice behavior. We find in model simulations that under early noise, contextual information enhances choice accuracy, while under late noise, context degrades choice accuracy. Furthermore, we verify these opposing predictions in experimental human choice behavior. Manipulating early and late noise - by inducing uncertainty in option values and controlling time pressure - produces dissociable positive and negative context effects. These findings reconcile controversial experimental findings in the literature, suggesting a unified mechanism for context-dependent choice. More broadly, these findings highlight how different sources of noise can interact with neural computations to differentially modulate behavior.