We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents $\gamma$ and $\nu$—depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase—concur to determine the potential divergency of a dynamic response, epitomized by the center-of-mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.

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• Anomalous diffusion
• Critical phenomena
• Polymers
• Langevin equation
• Master equation
• Renormalization group