Industrial production systems must continuously adapt to changes in product mix, machine states, and workforce availability. The ability to swiftly generate new production system layouts and process plans to respond to disruptions is essential. This work introduces a breakthrough two-stage constraint-guided difusion model that realizes fully automatic, hierarchical industrial layout generation with strict feasibility guarantees. An automatic synthesis is developed by combining a plant-level flow graph with processing stations, bufer stations, assembly and disassembly stations, together with a station-level graph capturing the detailed behavior for each station. The framework trains two discrete difusion models: one learns the global topology, and the other, conditioned on station type, learns internal Petri net representations for individual stations. A projector is defined to enforce a set of structural and dynamic constraints at every denoising step. The method delivers 100% validity under three progressively constrained inventory scenarios and preserves 99% uniqueness according to the Weisfeiler-Lehman hash. A complete hierarchical layout can be generated in approximately 2 seconds, and simulation-based evaluations confirm the operational competitiveness of the generated designs.
Smart factories reconfigure material flows and resources on-line during production to adapt to disruptions afecting the availability of resource and external signals. Yet, designing alternative layouts that always meet connectivity, capacity, and control rules is still largely manual and error-p1r,o2n]e. [
This work focuses on the problem of automatically synthesizing alternative plant layouts that respect a
set of constraints governing the use of resources and the flow of materials. Classical optimization (mixed
integer programming, graph grammars, metaheuristics) scales poorly and transfers little knowledge
across projects3[
We close this gap with a constraint-guidehdierarchical difusion framework. An entire plant is
disassembly machines. Every non-bufer station embeds a Petri net that captures local concurrency,
blocking, and resource contention12[
CEUR
ceur-ws.org lower level the details of each station using Petri net formalism. Two hard projectors act after every reverse step: the industrial projector enforces machine–bufer pairing and correct in/out degrees for assembly and disassembly machines; the Petri projector guarantees strict place–transition alternation. The sample thus remains inside the feasible set throughout the trajectory.
Experiments on 300 synthetic factories show that the model delivers 100% validity, 86–99% structural uniqueness, and realistic throughput–energy trade-ofs. Omitting the projectors reduces validity below 1%, confirming their necessity. To our knowledge, this is the first difusion approach that unifies multi-level industrial topology synthesisand embedded control-logic generation, paving the way for fully automatic, constraint-aware factory design in the AI era.
Difusion background. Let z0 be a categorical encoding of a graph (node labels and adjacency). A discrete forward kerne(lz+1 ∣ z ) = (1 − ) z + u, with u the uniform distribution over th e categories (her e is the number of possible node/edge classes), progressively randomizes the graph for = 0, … , −1 . The reverse process lear n s(z−1 ∣ z ) = Cat( (z , ) ), where is the neural network that outputs logits for the Categorical distribution, and samples by denoising fzro∼mu back toz0. In our settingz = ( , ) combines the station types and the edge tenso r .
Hierarchical plant representation. We formally define our modeling framework as follows. A factory layout is a two–level directed grap=h ( , , , ) : the plant layer contains stations labeled by ∈ { processing machine, bufer , assembly machine, disassembly machine} and each non-bufer station embeds a Petri net = ( , , ) with ∈ { place, transition}. Seven hard rules (degree limits, bufer isolation, acyclic flow, place–transition alternation, etc.) define the feasibility seℱt.
Dual difusion with hard projection. First, at the plant level a lightweight graph-transformer (two TransformerConv layers, ℎ=12) predicts updated logits for station labels and inter-station edges; the industrial projectoΠrpl then clips or flips entries so that global constraints—one-to-one processing–bufer pairs, correct in/out degrees for assembly and disassembly machines, and the prohibition of bufer–bufer arcs—already hold before the next iteration. At the station level three identical denoisers, each conditioned on its parent’s type, generate the internal Petri nets of processing, assembly, and disassembly machines; the Petri projectoΠrpet removes self-loops and enforces the strict place↔transition alternation that guarantees safe dynamics. A bufer degenerates to a single place and therefore bypasses the station-level chain. Projection after every reverse step keeps the sample insℱid,eso the ifnal graph is always valid.
With a random timestep ∈ {0, … , −1} we corrupt the clean grap(h , ) into ( ̂ , ̂ ) and minimize ℒ = CEnode + CEedge + KL KL( ‖ data) + ℒproj, whereCEnode andCEedge are cross-entropy terms that force the network to reproduce the true node labels and adjacency matri x from the noisy inputs; the KL termKL( ‖ data) keeps the one-step reverse marginals aligned with the empirical class frequencies, curbing early-step mode collapse; and ℒproj sums the probabilities assigned to edges that are forbidden by the industrial or Petri-net grammar, thereby penalizing structural violations. The positive scalaKrLs and control the strength of the KL regularizer and the structural penalty, respectively.
Conditional sampling. Masks let us(i) free generate,(ii) pin the exact inventory, or(iii) partially pin any subset of stations. Pinned labels remain unchanged while the stochastic chain and projectors drive the rest toward a consistent layout. Generating 1 000 hierarchical graphs (15–40 stations each) costs 21 min on commercial GPU.
We produced three batches of three hundred layouts each: free generation, full inventory pinning, and partial pinning of the stations. Every layout satisfied the seven structural rules and the Petri-net typing checks, confirming that the projectors keep the difusion trajectory inside the feasible set. Uniqueness, measured with the Weisfeiler-Lehman hash, remained high: approximately 86% for the free run and 89% when the inventory was fixed, showing that the model still explores a broad solution space even when strong priors are imposed. Maximum-mean discrepancy stayed below 1.3 in all cases, indicating that node-type frequencies and edge density match the training distribution (Ta1b).le
Operational realism was gauged with a discrete-event simulator that ran each plant for ten thousand time steps with stochastic, type-specific processing times. Throughput and energy use were recorded at every tick. As Figure1 shows, the generated layouts cover the same throughput-versus-energy frontier as the training set: fully pinned samples cluster on the energy-eficient side, whereas free samples explore a broader range, including high-throughput, high-energy outliers. These results indicate that the model produces layouts that are not only structurally valid but also operationally plausible.
We presented a hierarchical difusion framework that combines plant-level and station-level generators with hard projectors, producing industrial layouts that are valid and semantically consistent at every step. Systematic ablations confirmed that the structural projector is essential for handling the combinatorial constraints, while a modest network width of six to twelve hidden units already delivers high structural fidelity and realism. Complementary simulation-based evaluations further show that the generated layouts achieve favorable throughput and energy eficiency, even without explicit performance supervision.
Future research will scale the approach to real factory data and investigate adaptive, learnable constraint sets. In particular, recent large-language-model reasoning could be leveraged to express context-sensitive semantic rules on demand, giving designers even greater flexibility and precision when generating industrial plant layouts.
During the preparation of this work, the authors used ChatGPT-4o in order to: Grammar and spelling check. After using these tool/service, the authors reviewed and edited the content as needed and takes full responsibility for the publication’s content.