Diffusion models, exemplified by Stable Diffusion, provide a robust technical foundation for the generative design of urban form. In the early stages of exploration in computer vision and computer graphics, attempts were made to generate morphological patterns using probabilistic models (Sen et al., 2012).

Scholars such as Gu et al. (2024) and Kapsalis (2024) have leveraged the unique iterative denoising mechanism of diffusion models to open up a new avenue for the algorithmic generation of urban form. Subsequently, researchers including Cui et al. (2024) and Shi et al. (2024) have refined the theoretical framework and technical specifications of generative models, enabling them to generate complex and visually realistic urban form images based on diverse input conditions. Jiang et al. (2023) note that diffusion models can unravel the intricate relationships between urban form elements by learning feature distributions in high-dimensional spaces, thereby generating spatially coordinated layouts. Various studies have validated the significant effectiveness of diffusion models in rapidly generating a wide range of planning schemes (Yu et al., 2024; Zhuang et al., 2024). Ideally, the urban configurations generated by diffusion models should accurately align with local spatial characteristics. However, existing research fails to adequately incorporate region-specific elements such as street textures and local architectural symbols, and lacks systematic investigation into the biases in the expression of local features.

To address the limitations of diffusion models in capturing regional features, this study introduces the LoRA (Low-Rank Adaptation) technical framework. In 2022, Hu, E. J. et al. proposed the LoRA method while researching efficient fine-tuning of large-scale pre-trained models (Hu et al., 2022). Its core principle involves modifying model parameters through low-rank matrix factorization, achieving targeted optimization by adjusting only a small number of parameters. Subsequent studies have expanded the application scope of this technology to fields such as image generation and natural language processing, confirming its significant role in improving model performance in specific scenarios (Luo et al., 2024; Yu et al., 2023). This study explores the integration of LoRA and diffusion models, aiming to enhance the model’s ability to perceive and express local quantitative spatial characteristics through parameter optimization. Previous research has examined this technical pathway at various levels (Sun et al., 2022; Wang et al., 2024; Zhang et al., 2022). LoRA can accurately identify the quantitative hierarchical features of a specific dataset while preserving the generative capabilities of the underlying model, thereby aligning the model’s output more closely with the requirements of the target scenario. At the application level, studies have verified that LoRA contributes to improving the precision of local details in image generation tasks, particularly in contexts such as style transfer and element matching (Kim et al., 2024). However, existing research primarily focuses on the broad field of image generation, with limited specialized exploration of the adaptability and effectiveness of quantitative fine-tuning in urban form generation.

Urban form, as the tangible embodiment of urban functions and cultural significances, constitutes the central focus of inquiry in urban planning, geography, and landscape ecology. The initial measurement of urban form depended on basic geometric metrics, including urban compactness and shape index (Burgess and Jenks, 2000). Nevertheless, these indicators merely represent the city’s general framework and fail to convey the underlying spatial configuration and functional arrangement, so complicating the depiction of the urban system’s complexity. Subsequently, quantitative methodologies rooted in landscape ecology gained prominence (Tian et al., 2022). The Landscape Pattern Index was originally utilized to examine the spatial arrangement of natural ecosystems and gained widespread application for its capacity to delineate the composition, layout, and connectedness of urban patches (Jia et al., 2019). It can be categorized into patch level, type level, and landscape level based on scale (Wu et al., 2023). This study explores the relationship between landscape pattern indices and regional geometric features to assess the degree of integration of regional traits into local form design and their impact on such design. In this study, quantified regional attributes are used to define the core connotations of morphological locality.

Landscape sustainability science reveals that the composition and configuration of landscape patterns are key links connecting local morphological features with the global Sustainable Development Goals (SDGs). Empirical research has confirmed that Galan (2024) found through a comparative study of the landscape in Valencia that urban agglomeration, compactness, and other morphological characteristics significantly affect the functionality of ecological infrastructure, directly regulating the integrity and accessibility of urban green space coverage (Galan, 2024). Soltani et al. focused on spatial characteristics such as functional mix and distribution of public spaces, revealing the moderating effect of architectural spatial configuration on the relationship between social sustainability and urban density (Soltani et al., 2022). Lu et al. conducted a study on shrinking cities in Heilongjiang Province, which showed that landscape pattern indices (such as aggregation index AI, patch density PD, landscape shape index LSI, etc.) and transportation factors in spatial connectivity dimensions are effective elements that affect urban spatial performance (Lu et al., 2024).

This study utilizes Open Street Map as the primary map data source, excluding informal association data such as location labels and road network characteristics. For data filtering, only the “buildings” category features in the OSM database are retained to ensure the purity of the built environment-related information. The map data is transformed into a grayscale texture map, with white pixels denoting undeveloped areas such as agricultural land, green spaces, natural water bodies, and transportation infrastructure, while gray pixels signify built environments, including residential, commercial, and industrial zones. In terms of spatial projection, the dataset is georeferenced to the WGS 1984 geographic coordinate system, with all spatial information expressed in corresponding latitude and longitude values. The final processed map data has asquare plots of 20,000 pixels, covering a square area of 39.0625 km, which establishes a standardized training dataset for urban form analysis. This binary processing streamlines the hierarchical organization of image data and improves the spatial identification capacity of urban form.

The dataset chose all urban areas from eight cities—Singapore, Shanghai, Seattle, Paris, New York, London, Chicago, and Berlin—based on their spatial richness, morphological stability, and internal homogeneity characteristics. The geographic spatial map was first divided into square plots of 500 m on each side, and then a random window sampling method was adopted to extract 256 × 256 pixel images from these plots for subsequent model training and analysis. To eliminate interference from non-urban environmental elements such as water bodies, and to avoid the urban edge effect—such low-built-up-ratio samples are mostly located in the transitional zones on the urban periphery, and their morphological characteristics cannot represent the typical texture of the urban core built-up areas—samples with a built-up area proportion of less than 5% were deemed ineligible and removed from the analysis. Ultimately, we constructed a sample library with 10,000 city blocks that adhere to quality standards for each city. Among them, the division ratio of the training set to the validation set was set at 8:2. Table 1 shows the proportion of valid data for each city.

Existing research has confirmed that indicators such as the size, dimensions, and connectivity of urban space are closely related to sustainable urban development (Galan, 2024; Lu et al., 2024; Soltani et al., 2022). The landscape pattern index system of this study selected five widely recognized indicators from the five dimensions of shape, scale, compactness, fragmentation, and adjacency, forming a quantitative framework for characterizing urban form. Table 2 displays the chosen indicators, specifically tailored for built-up areas, which adeptly encapsulate the spatial configuration attributes of land use, building typologies, and street networks. The displayed urban form data is transformed into computable parameters, offering a mathematical foundation for assessing the impact of model prediction outcomes on sustainable urban development (Fan et al., 2023).

The meanings of the parameters for each index are as follows: a i j denotes the area of the j-th patch within the built-up area, and A denotes the total landscape area of the 500 m × 500 m research patch; E refers to the total perimeter length of all patches in the built-up area; g i j refers to the number of adjacent patches of the same type in the built-up area, which is calculated based on the 8-neighborhood rule. All the landscape pattern indices in this study were calculated using FRAGSTATS software (McGarigal and Marks, 1995), with the following calculation configurations: the 8-cell neighborhood rule was adopted, and the grid resolution was set to 1 m.

This research utilizes a standardized urban form dataset and employs the LoRA methodology to train a compact model adept at extracting urban form characteristics. LoRA is an efficient parameter fine-tuning method that fundamentally involves integrating a low-rank decomposition matrix into the key layers of the pre-trained model (Biderman et al., 2024). Specifically, for the weight matrix W ∈ R d × k in the pre trained model, LoRA does not directly update the original weights, but introduces two low rank matrices A ∈ R d × r and B ∈ R r × k to update the weights by an amount Δ W ∈ B · A , where r ≪ min d , k . This decomposition method reduces the number of parameters that need to be trained from d × k to r × d + k , usually only the traditional fine-tuning of 1 % ∼ 10 % .

The pre trained model selected for training is Anything v5, which performs well in structured scene feature extraction (Hugging Face, 2023). Its architecture includes three modules: CLIP text encoder maps text into high-dimensional semantic vector through Transformer; U-Net utilizes cross attention mechanism to fuse text and image features, and self attention mechanism to capture long-range dependencies of images; The VAE decoder maps potential features to pixel images based on variational inference, satisfying the p x | z = N x ; μ z , σ z 2 I distribution. Through LoRA fine-tuning, it can adapt to specific patterns of urban form, and its low rank matrix decomposition formula based on only updating the attention weights of key layers is as follows: W = W 0 + B A B ∈ R d × r , A ∈ R r × k , r ≪ min d , k

Among them, W 0 is the original pre-trained weight matrix, W is the adjusted weight matrix, B and A are the matrices obtained by low-rank decomposition, and r is the rank of the low-rank matrix and is much smaller than d and k . This formula can accurately target key features and make targeted adjustments to the attention weights of key layers, enhancing the model’s capture and learning of these features

The forward propagation process of the LoRA model can be expressed as: h = W 0 · x + α r · B · A · x

Among them, x is the input feature vector, α is the scaling factor. The introduction of scaling term α / r is used to balance the contribution ratio of the original weights and LoRA updates, ensuring the synergistic effect of pre trained knowledge and task specific features during the fine-tuning process. This mechanism enables the model to retain the ability to recognize general spatial features while enhancing sensitivity to core indicators such as density, clustering, and complexity when analyzing regional features.

The sample input adopts a random horizontal flipping and brightness perturbation enhancement strategy, which can be mathematically expressed as: x ′ = flip x with 0.5 , x + ϵ where ϵ ∼ N 0 , 0.02

Among them, flip x is the horizontal flipping operation, and ϵ is the brightness disturbance value that follows a normal distribution. The introduction of data augmentation has to some extent improved the robustness of the model to the spatial variation of urban form (Garcea et al., 2022).

The optimizer uses AdamW8-bit, and its core update formula is: m t = β 1 · m t − 1 + 1 − β 1 · g t v t = β 2 · v t − 1 + 1 − β 2 · g t 2 w t + 1 = w t − η t · m t v t + ϵ − λ · w t

Among them, m t and v t are the first-order and second-order moment estimates of gradient g t , respectively. β 1 = 0.9 , β 2 = 0.999 , λ = 0.01 are the weight decay coefficients, and ϵ = 1 e − 8 is the numerically stable term. In urban form training, the advantage of this optimizer lies in its efficient updating of sparse features. When the input contains a mixed block of rare forms such as high-density commercial areas and green spaces interwoven, Adam W8-bit’s adaptive gradient adjustment ability can quickly enhance the weight of the relevant low rank matrix (Dettmers et al., 2022). The entire model training process uses mixed precision BF16 calculation, and by using BFLOAT16 precision in key operations such as matrix multiplication, the impact of precision loss on training stability is avoided (Osorio et al., 2022). Table 3 lists the core parameters of LoRA low-rank fine-tuning after testing

This research develops a model for generating urban form features with a diffusion model, enabling accurate modeling of particular regional urban forms via LoRA fine-tuning. The fundamental premise is to produce images that correspond to the desired features from random noise using a progressive denoising procedure. The diffusion generation model is constructed using the LoRA model trained in Section 2.2, incorporating the landscape pattern index of urban form as a constraint to facilitate cross-modal generation from quantitative indicators to visual representation.

The model construction introduces landscape pattern index as a conditional constraint, converts the calculated landscape pattern index into text prompt embedding vector, and fuses it with image features through cross attention mechanism (Vaswani et al., 2017). Specifically, in each attention module of U-Net, semantic features corresponding to landscape pattern indices are added: Attention Q , K , V = Softmax Q K T + Q M T d k V

Among them, Q , K , and V are the query, key, and value matrices of image features, M is the semantic embedding matrix of mismatch index, and d k is the feature dimension. This mechanism enables the model to respond to the constraints of cities in dimensions such as shape, size, compactness, fragmentation, and adjacency during the generation process. Table 4 lists the relevant training parameters in the diffusion model

This study performed a multidimensional classification of regional geometric features for 10,000 standardized urban block samples in each city, employing quantitative thresholds of landscape pattern indices to clarify the distribution patterns of samples displaying diverse combinations of morphological traits. The classification system comprises five fundamental dimensions: density, aggregation, complexity, connectedness, and integrity. Table 5 illustrates that the categorization criteria for each dimension are determined by the statistical characteristics of the landscape pattern index.

This study employed the 25th and 75th percentiles of the boxplots for each indication as the primary criteria for categorizing morphological kinds. This categorization approach retains the morphological attributes of the predominant metropolitan areas, encompassing 50% of the feature regions, and differentiates them quantitatively. Table 6 presents the 25th and 75th percentiles of data for each city, demonstrating that the average building density in Paris and New York significantly exceeds that of the other six cities.

Figure 3 illustrates the progressive classification outcomes of the Singapore City Index. The categorization findings demonstrate that features from various dimensions display a markedly uneven distribution. High-density typologies are predominantly found in the eastern interior and southern coastal regions, reflecting the urban form’s regional geometric features shaped by industrial development and transit modalities. Samples of low density are concentrated around Bukit Timah Mountain and have overlapping correlations with low-class characteristics.

Figure 4 shows the indicator overlap rate for each city, with an overlap rate of 9.15‰ for low connectivity and high clustering, and 9.86‰ for low density and high clustering. Compared with the correlation values of other indicators in the same or across dimensions, this proportion is significantly lower, with an overlap degree of 27.46%, while the overlap degree of medium density and high clustering is 11.42%, which is the smallest; The overlap rate between medium density and medium aggregate is 9.49%. The entire related system exhibits a low proportion of overlapping features, further demonstrating the property of minimum overlap. This minimum overlap result sequence indicates that the indicators have substantial discriminative power in depicting various aspects of urban form. The proportion of landscape features emphasized by each indicator varies, providing a basis for examining landscape spatial organization from different perspectives.

In terms of the correlation between density and complexity, medium-density samples are typically associated with moderately complex morphologies, whereas low-density samples predominantly display complex or moderately complex traits. This pattern corresponds with the developmental logic of metropolitan regions—medium-density urban districts exhibit a degree of orderly spatial structures, whereas low-density peripheral areas have more intricate morphologies due to mixed functions and spatial dispersion. In terms of connection and integrity distribution, samples exhibiting poor connectivity typically have fragmented characteristics, whereas those with strong connectivity are predominantly associated with intact or reasonably intact features. This suggests that the interconnection of street networks is essential for preserving urban morphological integrity.

According to the structure of Table 5, discretize the form dimensions obtained in Section 4.1 into text prompts in the format of “City Name (Singapore), City Building Form Map”, Density indicators (High Density),Aggregation indicators (Highly Aggregated),Complexity indicators (Moderately Complex),Connectivity indicators (Medium Connectivity),Intact indicators (Medium Connectivity)”. Based on the corresponding dataset image training, a lora model with 100 epochs was selected to generate 800 indicator free prompt word images based on Singapore. The generated results are shown in Figure 5.

We conducted index analysis on the 800 generated images, and Figure 6 illustrates the index overlap rate of the generated results. The findings reveal that without using prompt words, the model converges to 25%–75% of the categories corresponding to the 5 indicators, accounting for a total proportion of 48.50%. Meanwhile, some indicators correspond to extremely low morphological proportions: the total proportion of generated images in the “Fragmented” category (matching 25% of the training data) is only 3.75%, while “Simple” also accounts for just 3.75%, “Low Connectivity” for 3.88%, and “Intact” for 4.63%.

These results indicate that all metrics of images generated by the Lora model (in the absence of prompt words) will be heavily concentrated in the 25%–75% middle range, leading to a clustered distribution of the generated images indicator profiles.

Use FID and SSIM metrics to evaluate and validate the overall model. FID evaluates the overall distribution difference between the created image and the real image, while SSIM evaluates the structural similarity of the image. The FID value of the created image and the validation set is 31.2998, while the SSIM value is 0.5880 ± 0.0350,with small variance, shows stable structural similarity, proving the model well preserves image structural details critical for realistic output.

Through the analysis of data relationships across various urban feature groups, based on the strict criteria of data integrity and quality—specifically, a total of 18 sets were produced for six cities: Singapore, Shanghai, Seattle, Paris, New York, and Chicago, with three outcomes created for each set, as illustrated in Figure 7. At the visual level, it can more accurately depict the morphological aspects of the target city across various urban regions. Subsequently, assess the coherence among these 18 sample sets and the anticipated output indicators, and evaluate the extent of alignment between the findings produced by the diffusion model and the established formal criteria. These indicators pertain to the structural integrity, functional coordination, and form recognition of urban space, serving as essential criteria for assessing the model’s capacity to “generate local forms” in urban planning contexts. Compute the landscape pattern index for each produced form, as seen in Figure 8 and Table 7.

The generation forms of various cities demonstrate significant spatial disparities, while the forms within the same city under differing parameters reveal considerable spatial diversity. Singapore and Shanghai frequently demonstrate significant intensification in spatial organization, characterized by relatively uniform arrangements of structures and communities, together with a balanced distribution of spatial density. This underscores the significance that Eastern cities attribute to intensive land utilization and the establishment of spatial organization in their developmental processes. This trait aligns with the historical growth context of densely populated cities in the East, where land resources are rather limited. The urban forms of Paris, New York, and Chicago display characteristic spatial structures, including radial and grid patterns, which are associated with historical urban planning concepts and influenced by factors such as transportation and functional organization in their development processes. Simultaneously, variations in spatial density, block scale, and open space proportion exist among different parameters within the same city, illustrating potential evolutionary trajectories of urban form under diverse development orientations, thereby offering a clear spatial representation for the dynamic optimization and sustainable development analysis of urban form.

Core indicators such as PLAND, LPI, LSI, PLADJ, and AI exceed 78%, resulting in an overall compliance rate of 85.72%, which demonstrates the robust efficacy of diffusion models in producing urban form data via essential landscape pattern indices.

This aggregate numerical performance illustrates the model’s efficacy in reproducing essential urban morphological characteristics. It encapsulates urban compactness via

PLAND, with elevated values signifying concentrated land use, a crucial attribute of effective urban spatial organization. This model, through LSI, encapsulates the intricacies of form and illustrates how location, history, and planning influence the authentic urban structure. LPI can replicate common structural characteristics found in actual cities, where the predominant expansive regions function as the urban nucleus. PLADJ and AI constitute a unified entity, augmenting the simulation of spatial connectedness and integrity: PLADJ facilitates effective patch integration, whereas AI mitigates fragmentation, collectively fulfilling the criteria for functioning and cohesive urban systems.

The deep learning-based conditional control generation model developed in this study exhibits considerable efficacy in producing urban shape depending on geographical characteristics. The findings demonstrate that the model aligns with the objectives of urban sustainable development, encompassing efficient land utilization and cohesive spatial arrangement, accurately representing the intricacies of real urban configurations, hence validating its efficacy in urban form simulation.

The model exhibits substantial consistency in the PLAND index, with all cities registering a PLAND value exceeding 80%, so illustrating the model’s strong regulation of the fundamental spatial structure of urban form. The systematic denoising process of the diffusion model aligns with the distribution pattern of urban form, accurately detecting benchmark aspects of varying urban patch area ratios, so offering dependable support for the overarching framework established by urban form. The conformance rate of all landscape pattern indices exceeds 78%, underscoring the model’s advanced self-learning capability about the interrelationship between urban form indices. The creation of urban form is fundamentally a process of spontaneous integration of regional attributes and natural surroundings.

Neglecting regional geometric features in urban design practice is a key driver of uneven global urban development, stemming from high costs in reconciling traditional landscape protection and development needs, and a lack of quantitative tools for integrating regional traits into decisions. Both new urban districts and renovated historic areas often erode local features, leading to urban homogenization, cultural identity loss, and hidden cultural costs.

The proposed conditional control urban form generation framework effectively addresses these issues by filling the quantitative assessment gap and linking form generation technology to regional trait preservation. Taking landscape pattern indices as input constraints, the model generates targeted form schemes. Higher PLADJ improves public transport accessibility and reduces carbon emissions, aligning with low-carbon goals. Adjusting AI links to land use mixing degree, fostering vibrant mixed-use spaces. This bridges technology and practice, enhancing the model’s guiding role in sustainable urban design. In real historic district renovation, inputting expected values enables generating multiple schemes; comparing these indices helps select designs that retain traditional spatial texture, providing a quantitative basis for balancing protection and development and enhancing design decision rationality. By quantifying geographical and cultural attributes, it supports evidence-based decisions, shifting design from experience-driven to data-supported.

This work refined the urban form generation model; yet, some limitations persist. This scenario presently pertains solely to established metropolitan regions, and its relationship with various geographical contexts, climatic conditions, and urban growth patterns remains unverified, potentially resulting in environmental disparities in other cities. The second issue is that LoRA fine-tuning employs a static parameter design, inhibiting dynamic adjustments of sensitivity according to the significance of indications. This complicates the fulfillment of diverse learning needs for fundamental features in intricate contexts, thereby impacting generation accuracy.

Future research can enhance multiple disciplines to tackle the previously outlined issues. The research scope transcends the constraints of individual city type models and consolidates representative morphological characteristic parameters from many locations to improve the model’s universality. Concerning the model architecture, a dynamic ranking method may be employed to assign weights according to the significance of indicators, while preserving regional geometric features and including diverse stylistic elements to enhance generation precision and innovative capacity.