Mold spores can form either through simple cell division, which is asexual, or through the fusion of two compatible structures, which is sexual. Sporangiospores are produced inside a sac like structure called a sporangium purely by asexual division, seen clearly in bread mould. Zygospores need the fusion of two similar gametangia, ascospores form inside an ascus after sexual fusion, and basidiospores form on a basidium, so all three are sexual in origin. That leaves sporangiospores as the only asexual spore type in the list.