We have developed a novel two-layer anti-reflection (AR) coating method for large-diameter infrared (IR) filters made of alumina, for the use at cryogenic temperatures in millimeter wave measurements. Thermally- sprayed mullite and polyimide foam (Skybond Foam) are used as the AR material. An advantage of the Skybond Foam is that the index of refraction is chosen between 1.1 and 1.7 by changing the filling factor. Combination with mullite is suitable for wide-band millimeter wave measurements with sufficient IR cutoff capability. We present the material properties, fabrication of a large-diameter IR filter made of alumina with this AR coating method, and characterizations at cryogenic temperatures. This technology can be applied to a low-temperature receiver system with a large-diameter focal plane for next-generation cosmic microwave background (CMB) polarization measurements, such as POLARBEAR-2 (PB-2).