Przemyslaw Musialski
1. Thesis
Generative models for the engineered world must carry the structure of that world inside the model. Built in, structure makes generation controllable, so that a designer can edit and steer the result, and certifiable, so that the result satisfies the constraints it can be rejected for violating. This does not depend on model size: a larger model is more capable and less inspectable, and in these domains the need for built-in structure grows with scale.
The claim applies where a result is judged by correctness rather than by plausibility. For images, text, and video, a result is good if it looks right, and scale has won that contest. For buildings, mechanical parts, fabricated structures, and design, a result is good only if a facade follows its grammar, a surface can be milled, a structure stands.
The alternative is to generate freely and enforce constraints afterward, by projection, optimization, or rejection. It works when violations are small and the object is simple. It fails when the repaired result is no longer what the designer asked for, when the repair is itself a hard optimization, or when nothing in the model says what to change. With structure inside the model, generation and constraint share one representation, and an edit is checked in the same step.
2. Foundations
I am a geometer. The thesis is the position I have held through twenty years of work on the geometry of the built and manufactured world. What has changed is the machinery underneath it. My doctoral work at TU Wien and VRVis was on reconstructing buildings from images. It produced a widely used survey of urban reconstruction (Computer Graphics Forum 2013) and interactive and procedural facade models (Eurographics 2012 and 2015, SIGGRAPH Asia 2014). With Leif Kobbelt I developed reduced-order shape optimization for fabrication-aware modeling (SIGGRAPH 2015 and 2016). At the Center for Geometry and Computational Design I founded the Computational Fabrication group and took elastic geodesic grids from differential geometry through optimization to physically deployed structures (SIGGRAPH 2020, SIGGRAPH Asia 2021, an Austrian patent). In each, the structure lived in the representation from the start, and the method was built on top of it. Since 2021 the method has been a learned generative model, and where the structure lives has become the central question.
3. The program since 2021
My group carries structure into generative models in three forms.
Procedural. A model that knows a facade's grammar generates and edits facades as programs rather than pixels. FaçAID (SIGGRAPH Asia 2024) is a transformer that turns a facade image into its procedural representation. Pro-DG (Computer Graphics Forum 2026) guides a diffusion model with the grammar, so the generated facade can be edited symbolically afterward. LayoutEnhancer (SIGGRAPH Asia 2022) encodes ergonomic rules as differentiable objectives inside a transformer generator for interior layouts.
Differential-geometric. For CAD models dominated by developable patches, zero Gaussian curvature provides a useful geometric prior. FlatCAD (Pacific Graphics 2025) regularizes neural signed distance fields toward developability with an off-diagonal Weingarten loss cheap enough to train with. The follow-up work (SIGGRAPH Asia 2025, ISVC 2025) studies how such priors should be scheduled and approximated.
Physical. This is where structure is most exact and where generative work is least advanced, mine included. My own physical line, from shape optimization on offsets to the elastic grids, has produced printed and deployed objects whose properties were designed rather than checked. Making that generative is the next step.
My contribution to the generative machinery itself is Beyond Blur (ICCV 2025), a fluid-dynamics reading of diffusion models that yields a new family of forward processes. With Zhi Wei at NJIT we used implicit neural fields to align spatial transcriptomics data into a 3D volume (MICCAI 2026).
4. Where the program goes
The next stage sits on the seam where learned geometry stops and engineering begins. Two directions follow from the work above. The first is generators that emit programs rather than coordinates, so that the written requirements of a domain, building codes and design handbooks for layouts and facades, can be stated on the output exactly, trained on, and preserved through an edit. The second is neural signed distance fields that are solids in the engineering sense, with sign and distance reliable away from the surface, so that offsets, shells, Boolean operations, and mass properties can be computed on the learned field itself and the result can be fabricated and measured.
If the program succeeds, an engineer or an architect asks a generative model for a part, a facade, or a floor plan, edits it in the language of their own discipline, and reads from the same object whether it can be built, with the verification inside the representation rather than in a separate step.