There is described a foamed isocyanate-based polymer derived from a reaction mixture comprising: an isocyanate; a polyol composition comprising a first prescribed amount of polymer particles dispersed in a base polyol; a second prescribed amount of biomass-based carbonaceous particulate material; and a blowing agent. In one embodiment, the foamed isocyanate-based polymer having an Indentation Force Deflection when measured pursuant to ASTM D3574-11 which is within about 15% as that of a reference foam produced by omitting the biomass-based carbonaceous particulate material from the reaction mixture and increasing the amount of polymer particles in the polymer polyol composition to equal the sum of the first prescribed amount and the second prescribed amount. In another embodiment, the foamed polymer has a cellular matrix comprising a plurality of interconnected struts, the biomass-based carbonaceous particulate material conferring to the cellular matrix a load efficiency of at least about 5 Newtons/weight % of biomass-based carbonaceous particulate material. A process to produce the foamed isocyanate-based polymer is also described. A polyol-based dispersion to produce the foamed isocyanate-based polymer is also described. It has been discovered that a relatively expensive petroleum-based copolymer polyol can be fully substituted by a relative inexpensive bio-based (amorphous carbon) dispersion with no significant compromise in important physical properties in the resulting polyurethane foam.