The climate crisis is urging us to act fast. Buildings are a key leverage point to reduce greenhouse gas (GHG) emissions, but the embodied emissions related with their construction remain often the hidden challenge of any ambitious policy. Considering that a complete material substitution is not possible, we explore in this paper a material GHG compensation where fast-growing bio-based insulation materials are used to compensate building elements that necessarily release GHG. Looking for analogies with other human activities, different material diets as well as different building typologies are modelled to assess the consequences in term of bio-based insulation requirement to reach climate-neutrality. The material diets are defined according to the gradual use of herbaceous materials, from the insulation up to the structural level: omnivorous, vegetarian and vegan. Our results show the relationship in terms of volume between the climate intensive materials and the climate-negative ones needed to neutralize the overall building GHG emissions. Moreover, they suggest how climate-neutral building can look like and that it is possible to have climate-neutral buildings with wall thickness within the range of current construction practices.