Many forms of synaptic plasticity require the local production of volatile or rapidly diffusing substances such as nitric oxide. The nonspecific plasticity these neuromodulators may induce at neighboring non-active synapses is thought to be detrimental for the specificity of memory storage. We show here that memory retrieval may benefit from this non-specific plasticity when the applied sparse binary input patterns are degraded by local noise. Simulations of a biophysically realistic model of a cerebellar Purkinje cell in a pattern recognition task show that, in the absence of noise, leakage of plasticity to adjacent synapses degrades the recognition of sparse static patterns. However, above a local noise level of 20%, the model with nonspecific plasticity outperforms the standard, specific model. The gain in performance is greatest when the spatial distribution of noise in the input matches the range of diffusion-induced plasticity. Hence non-specific plasticity may offer a benefit in noisy environments or when the pressure to generalize is strong.