Abstract: High training costs of generative models and the need to fine-tune them for specific tasks have created a strong interest in model reuse and composition.A key challenge in composing iterative generative processes, such as GFlowNets and diffusion models, is that to realize the desired target distribution, all steps of the generative process need to be coordinated, and satisfy delicate balance conditions.In this work, we propose Compositional Sculpting: a general approach for defining compositions of iterative generative processes. We then introduce a method for sampling from these compositions built on classifier guidance.We showcase ways to accomplish compositional sculpting in both GFlowNets and diffusion models. We highlight two binary operations $\\unicode{x2014}$ the $\\textit{harmonic mean}\\unicode{x00A0}(p_1 \\otimes p_2$) and the $\\textit{contrast}\\unicode{x00A0}(p_1 \\,\\unicode{x25D1}\\,\\, p_2$) between pairs, and the generalization of these operations to multiple component distributions.We offer empirical results on image and molecular generation tasks. Project codebase: https://github.com/timgaripov/compositional-sculpting.