Passage of polymers through pores narrower than the hydrodynamic diameter is impeded by an entropic penalty for their confinement. This might be balanced by an attractive interaction with the pore walls. We found that the hydrogen-bonding polymer, poly(isopropylacrylamide) (pNIPAM), diffused readily through narrow pores in polycarbonate track-etched membranes. The trons side accumulation of pNIPAM followed a stretched exponential behavior. By contrast, a much smaller dextran diffused at a comparable or slower rate and showed ordinary Fick-like behavior. Comparison between the influence of pNIPAM surface adsorption and chemical grafting to the pores points to weak interpolymeric bonds as the source for the transport-accelerating surface interactions. We interpret the results as evidence for anomalous diffusion of pNIPAM inside the pores.