Coarse-to-Fine Latent Guidance: A Multi-Scale Diffusion Transformer for Traffic Flow Forecasting

1 Introduction

Traffic flow forecasting (TFF) constitutes the cornerstone of modern Intelligent Transportation Systems (ITS), enabling critical downstream applications ranging from congestion mitigation [Lana et al., 2018] and resource optimization [Liu et al., 2023] to the facilitation of sustainable urban mobility [Maimaris and Papageorgiou, 2016]. While urban traffic exhibits inherent periodicity driven by daily commutes and societal routines, the underlying dynamics are deeply stochastic and non-linear [Ma et al., 2020; Wang et al., 2021]. Real-world flows are governed by a complex interplay of spatial-temporal dependencies, where stable global patterns are continuously modulated by volatile perturbations and external factors [Carianni and Gemma, 2025]. Consequently, achieving high-fidelity predictions remains a formidable challenge despite the apparent regularity of the data.

∗Corresponding authors.

Due to the complex spatial-temporal patterns of TFF, existing methods predominantly rely on deep learning [Manibardo et al., 2021]. Within this domain, Transformer-based approaches primarily focus on identifying long-range dependencies, utilizing attention mechanisms to connect distant spatial and temporal events that influence current traffic conditions [Jin et al., 2023; Jiang et al., 2023; Cai et al., 2024]. In parallel, diffusion models address the inherent uncertainty of the system. Instead of producing a single deterministic prediction, these generative frameworks learn the full probability distribution of traffic states, allowing them to better handle noise and missing data [R¨uhling Cachay et al., 2023; Wen et al., 2023; Fan et al., 2024; Hu et al., 2024a].

Despite these methodological advances, current models still fail to capture the natural multi-scale physical structure of traffic data, specifically the hierarchical dependency where stable global trends govern stochastic local fluctuations. As illustrated in Fig. 1, this hierarchy manifests as a complex superposition of distinct temporal behaviors. For the coarse scale, the average heatmaps (b) reveal a stable "skeleton"-robust low-frequency patterns governed by weekly routines that clearly differentiate the functional rhythms of distinct regions, such as the airport dynamics of Node A versus the arterial intersection patterns of Node C. Conversely, for the fine scale, the time series (a) exposes the stochastic reality: jagged high-frequency fluctuations superimposed on, yet structurally constrained by, these stable trends. However, existing methods ignore this intrinsic dependency. GNNs often aggressively over-smooth high-frequency details to capture spatial consistency [Choi et al., 2022; Kong et al., 2024], while monolithic diffusion models treat generation as a flat, isotropic process. By attempting to denoise all frequencies simultaneously without structural prioritization, they fail to anchor the prediction to the global context, often leading to unstable or physically inconsistent results [Fan et al., 2024]. This motivates our research: accurate forecasting requires a hierarchical framework that explicitly uses stable coarsegrained trends to guide the generation of fine-grained details.

To realize this, we propose the Multi-Scale SpatialTemporal Diffusion Transformer (MS-STDT). Our framework is founded on the spectral alignment between physical data and generative physics. We frame the multi-scale hierarchy as the intrinsic resolution trajectory of the diffusion process: since the forward injection of noise functions as a coarse-graining operation that naturally dissipates fine details while retaining global trends, the reverse denoising process logically mirrors this hierarchy through a structured coarseto-fine reconstruction. Consequently, the generative trajectory prioritizes recovering robust low-frequency structures in early sampling steps to establish a stable physical skeleton, effectively constraining the subsequent restoration of volatile high-frequency fluctuations. Guided by this insight, we employ hierarchical spatial-temporal encodings to represent distinct levels of granularity and introduce the Coarse-to-Fine Latent Guidance mechanism. This module mathematically aligns the diffusion steps with the data's physical hierarchy, using intrinsic macro-trends as a structural anchor to stabilize the generation. Finally, we incorporate a cross-scale attention mechanism to orchestrate the interaction between resolutions, dynamically re-weighting information flow to adaptively focus on broad trends or local variances as traffic conditions evolve.

To rigorously validate our framework, we conducted extensive experiments across six real-world datasets, benchmarking MS-STDT against 12 state-of-the-art baselines. These evaluations extend beyond standard accuracy metrics to specifically stress-test the model's zero-shot robustness against sensor failures and assess its computational efficiency.

Our contributions are summarized as follows:

• We identify a critical coarse-to-fine dependency in traf-
• fic data, where stable global trends serve as structural anchors for local fluctuations. This finding challenges flat modeling paradigms, demonstrating that robust forecasting requires explicitly disentangling these conflicting multi-scale resolutions.
• We propose the MS-STDT featuring Coarse-to-Fine Latent Guidance. By leveraging intrinsic data structures to guide the diffusion process, our framework effectively reconciles global consistency with local stochasticity without requiring external labels.
• Extensive evaluations on six benchmarks confirm that MS-STDT consistently outperforms existing baselines, improving MAE by 10.1% and CRPS by 12.8%. Beyond accuracy, the results highlight the model's exceptional zero-shot resilience to sensor failures.

2 Preliminaries

2.1 ProblemFormulation

We represent the topology of the road network as a directed graph G = (V, E,A), where V is a set of N nodes (sensors or intersections), and A ∈ RN×N denotes the weighted adjacency matrix encoding spatial connectivity. The dynamic state of the system is captured by the traffic flow tensor X = (X1, . . . ,XT ) ∈ RT×N×D , where Xt represents the D-dimensional traffic features at time step t.

Traffic flow prediction seeks to forecast future traffic states based on historical data. Specifically, the objective is to model the conditional distribution of future time steps (Xt0 , · · · ,XT ) given a historical context window and a graph. Formally, the problem can be formulated as:

Unlike deterministic approaches that output a single point estimate, this probabilistic formulation allows us to capture the stochastic uncertainty inherent in complex traffic dynamics.

2.2 Background: Conditional Diffusion

To model the complex distribution of traffic flows, we adopt the Denoising Diffusion Probabilistic Model (DDPM) [Ho et al., 2020] as our generative backbone. While standard DDPMs generate samples from pure Gaussian noise, traffic forecasting requires conditioning on historical states. Therefore, we align our approach with the autoregressive formulation introduced in TimeGrad [Rasul et al., 2021].

In this framework, the temporal dependencies are managed by a recurrent component (RNN) that summarizes the history X1:t-1 into a hidden state ht-1. The diffusion process is then applied to the current observation Xt conditioned on this state. The training involves a forward diffusion process that gradually corrupts Xt into Gaussian noise xnt over N steps, and a parameterized reverse process that learns to denoise it. Instead of predicting the clean data directly, we train a denoising network ϵθ to estimate the noise component added at each step. The training objective minimizes the reweighted variational bound:

where n is the diffusion step, ¯αn follows a fixed variance schedule, and ϵ ∼ N(0, I). (See Appendix A for the full derivation of the variational lower bound and transition kernels). This design allows the model to generate diverse and realistic future flow by iteratively refining random noise under the guidance of historical traffic patterns.

3 Methodology

3.1 Framework Overview

As shown in Fig. 2, MS-STDT framework operates through a progressive, coarse-to-fine strategy comprising five core components:

1. Multi-Scale Sampling (MSS): Instead of processing raw data X solely at its finest resolution, we project it into a latent space Xdata and progressively downsample it via strided convolutions. This yields a hierarchy of representations Xms = {X0data , . . . ,XMdata}, where the g-th scale Xgdata captures dynamics at a temporal resolution of T/2g . The sampling process is recursively defined as Xgdata = Conv (Xg-1 data , stride = 2) for g ∈ {1, . . . ,M}, allowing the model to explicitly decouple macro-trends from micro-variations.
2. Contextual Embedding: To ground these representations in physical space and time, we augment the data features with a composite embedding. We sum learnable Laplacian eigenvectors Xgspe (encoding graph topology [Belkin and Niyogi, 2003]), periodic embeddings Xgw ,Xgd (capturing weekly and daily cycles [Ding et al., 2023]), and temporal positional encodings Xgtpe [Vaswani et al., 2017]. The final input at each scale is defined as: Xg = Xgdata +Xgspe +Xgw +Xgd + Xgtpe.
3. Spatial-Temporal Process Module (STPM): Serving as the conditional encoder, this module operates independently at each scale g. It utilizes a unified masked attention mechanism to extract robust spatial-temporal features Cg , ensuring the model remains resilient to sensor failures and missing data.
4. Guided Diffusion Process Module (GDPM): This serves as the generative engine of our framework. Unlike standard diffusion models that treat denoising as a flat, isotropic task, GDPM utilizes the multi-scale representations as structural anchors. This allows the reverse process to stabilize the generation of fine-grained details by conditioning on the coarser, more stable trends.
5. Multi-Scale Fusion and Output (MSFO): Finally, we synthesize the predictions across all resolutions. An adaptive attention mechanism dynamically weights the generated samples Sg from each scale, fusing them into a single, cohesive forecast: Output = Ensemble ({Attng(Sg )}Mg=0 ) .

3.2 Spatial-Temporal Process Module (STPM)

Functioning as the scale-specific encoder, the STPM operates independently at each resolution g to extract robust features for the diffusion process. To distinguish intrinsic sparsity (e.g., low volume) from extrinsic missingness (e.g., sensor failure), it employs a unified masked modeling strategy. By forcing the reconstruction of randomly masked tokens via spatial-temporal context, the module ensures that structural dependencies are preserved across the hierarchy-guaranteeing that both stable macro-trends and stochastic micro-variations are accurately encoded even in the presence of sensor failures.

Unified Masking Strategies. We employ a diverse set of masks, each designed to teach the model a specific dependency: Local Robustness: Random Masking (Mrand) drops random patches to encourage local interpolation [Feichtenhofer et al., 2022]. Sensor Reliability: Tube Masking (Mtube) hides specific nodes across all time steps, simulating sensor outages [Yuan et al., 2024]. Global Context: Block Masking (Mblock) removes large contiguous regions, forcing the model to infer states from distant global signals [Li et al., 2022a]. Topology Awareness: Short/Long Masking (Mshort, Mlong) selectively hides neighbors based on graph distance, refining spatial propagation [Jiang et al., 2023]. Forecasting Capability: Future Masking (Mfuture) strictly hides future steps, aligning the training objective with the autoregressive nature of forecasting [Tan et al., 2023].

Masked Attention Mechanism. To process these masked inputs, we utilize a factorized attention mechanism. For a given scale embedding Xg , we compute attention separately along the spatial and temporal axes. Let Xgt:: andXg:n: denote temporal and spatial slices, respectively.

Spatial and Temporal Mask Attention. We adopt masked attention mechanisms to encode structured priors in both spatial and temporal dimensions. For each attention head g, we first construct the query, key, and value matrices as:

Here, the subscripts t and n denote temporal step and spatial node, respectively. Then masked attention scores and outputs are computed as:

where MS ∈ {Mrand,Mtube,Mblock,Mshort,Mlong}, MT ∈ {Mrand, Mtube, Mblock, Mfuture}.

Multi-Head Fusion. To fully integrate diverse spatial and temporal dependencies while maintaining computational efficiency, we apply multi-head attention across various masking strategies. Each head focuses on a specific aspect of the data, and their outputs are concatenated and linearly projected to multi-scale coarse-graining operation. As the diffusion steps advance and noise intensity increases (from step 0 to N), fine-grained high-frequency details dissipate first, leaving behind only the robust low-frequency structural information. We leverage this inherent property to formalize a direct mapping between the intermediate latent variables of the diffusion chain and the coarser resolutions of our data hierarchy. By explicitly anchoring specific diffusion time-steps to their corresponding multi-scale representations, we guide the model to reconstruct the stable global skeleton before refining the local details.

Coarse-Scale Guidance via Anchor Points. Let q(x0 ) denote the distribution of the finest-scale data (g = 0). A standard forward process q(x01:N |x00 ) corrupts this data into noise over N steps. To inject structural guidance, we identify specific intermediate steps N g ∗ ∈ [1,N -1] as anchor points for each coarser scale g.

We enforce that the latent state xN g ∗ at this anchor step must be consistent with the observed coarse-scale data xg . Formally, we optimize the model to maximize the likelihood of the coarse observation at this specific noise level. The marginal distribution of the latent variable xN g ∗ is defined as:

where xN ∼ N(0, I), and each reverse transition is modeled as a Gaussian: pθ (xn-1 | xn) = N (xn-1;µθ(xn, n), σθ(xn, n)) . To enable tractable optimization, a standard approach is to maximize the variational lower bound of the log-likelihood in Eq. 6. This can be

form the final representation.

where Concat(·) denotes concatenation, and W l is a learnable projection matrix. Following the standard Transformer architecture, the fused output is passed through a positionwise feed-forward network, with residual connections and layer normalization applied to stabilize training and enhance representational capacity. The resulting feature representation is denoted as Xo ∈ RT×N×d . Subsequently, a 1 × 1 convolutional projection is employed to map Xo into a conditional embedding Cg ∈ RT×N×dc , which serves as the scale-specific spatial-temporal representation.

3.3 Multi-Scale Guided Diffusion

Standard diffusion models typically neglect the intrinsic multi-scale nature of traffic data, treating the generative process as a monolithic mapping from noise to data. However, traffic flow exhibits a distinct hierarchical structure where stable global trends at coarse scales provide the foundation for local fluctuations at fine scales. To align the generative mechanism with this physical reality, we propose the Guided Diffusion Process Module (GDPM).

The core design principle of our approach is that the forward diffusion process, characterized by the progressive injection of Gaussian noise, is functionally analogous to a achieved by introducing a sequence of latent variables of length N - N g ∗ , which connects the observed coarse-scale data xg to the generative process. Specifically, we define a forward diffusion process over xg consisting of N-N g ∗ steps, producing a sequence of noisy variables xgN g ∗+1 , . . . , xgN . Under this construction, the log-likelihood of the observed coarse sample can be expressed as:

Following the DDPM framework [Ho et al., 2020], this objective simplifies to minimizing the denoising error at the anchor steps:

where xgn = (∏ni=N g ∗ α1 i ) xg + √1 - ∏ni=N g ∗ α1 i ϵ and ϵ ∼ N(0, I) (see Appendix C for full derivation).

Defining the SharingRatio andAnchor Steps. Determining the optimal anchor step N g ∗ is critical to ensure coarse guidance aligns with natural diffusion dynamics. We quantify this via the Sharing Ratio rg := 1-(N g ∗-1)/N. Thismetric formalizes the spectral correspondence between the diffusion process (acting as a progressive low-pass filter) and the data hierarchy. By serving as a normalized coordinate, rg maps discrete physical scales onto the generative timeline, identifying the precise window where coarse guidance is structurally homologous to the latent state.

To avoid arbitrary hyperparameter tuning, we propose a data-driven heuristic to determine N g ∗ . We posit that the optimal anchor step is where the signal complexity of the noisy fine-scale data matches that of the coarse data. Mathematically, we select N g ∗ by minimizing the Kullback-Leibler (KL) divergence: N g ∗ := argminnDKL (q(xg ) || pθ(x0n )) .

In practice, we estimate this by pre-training a baseline model and selecting the step n where the Continuous Ranked Probability Score (CRPS) between the generated sample and the ground-truth coarse data is minimized. This ensures that guidance is applied exactly when the diffusion process is naturally resolving features at that specific resolution.

Multi-Scale Objective. With the anchor points defined, we construct a scale-specific variance schedule αgn . For steps n ≤ N g ∗ , we set αgn = 1 (no noise added), effectively treating the coarse data as "clean" relative to that noise level. For n > N g ∗ , it follows the standard schedule:

We assume a strictly increasing hierarchy of anchor steps: N 0 ∗ < N 1 ∗ < · · · < N M ∗ , ensuring that coarser scales enter the diffusion process later. The final training objective aggregates the losses across all scales, weighted by ωg :

where Cg is the robust context representation from the STPM. This formulation ensures that the model simultaneously learns to generate accurate global trends (via high N g ∗ layers) and precise local details (via the g = 0 layer).

Inference. During inference, we generate predictions recursively. Starting from the end of the historical context t0 - 1, we sample predictions Xgt0 for each scale g. This process is repeated for the entire horizon [t0, T], producing a complete set of multi-scale predictions Sg .

4 Experiments

4.1 Experimental Settings

Datasets. MS-STDT is evaluated on three graph-based benchmarks (PeMS04/07/08 [Song et al., 2020]) and three grid-based benchmarks (NYCTaxi [Liu et al., 2020], CHIBike [Wang et al., 2021], and T-Drive [Pan et al., 2019]); dataset details are summarized in Tab. 1. The forecasting horizon is fixed to 24 steps for all datasets.

Evaluation Metrics. We adopt five widely used metrics for evaluation: Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) for deterministic accuracy, as well as Continuous Ranked Probability Score (CRPS) for probabilistic prediction.

Baselines. We evaluate the predictive performance of MSSTDT against three categories of strong baselines: (1) Diffusion-based models, including TimeGrad [Rasul et al., 2021], D3VAE [Li et al., 2022b], MG-TSD [Fan et al., 2024], DiffSTG [Wen et al., 2023], USTD [Hu et al., 2024b], UrbanDiT [Yuan et al., 2025] (2) Pretrained and self-supervised models, such as ST-SSL [Ji et al., 2023], UniST [Yuan et al., 2024], STD-MAE [Gao et al., 2024]; (3) Transformer- and MLP-based models, including BasisFormer [Ni et al., 2023], TimeMixer [Wang et al., 2024], STDN [Cao et al., 2025].

Parameters Settings. MS-STDT is trained for 100 epochs using the Adam optimizer with a learning rate of 10-5 . The batch size is conFig.d to 64 for the CHIBike dataset and 32 for all other datasets. All experiments are conducted on a single NVIDIA A100 GPU (40 GB) with 128 GB of memory using PyTorch 1.10.1 on Ubuntu 18.04.

4.2 Main Results

Table 2 presents the quantitative comparison of MS-STDT against 12 competitive baselines across six diverse benchmarks. The results demonstrate that our framework establishes a new state-of-the-art, consistently achieving the lowest error rates across all datasets and metrics.

Deterministic ForecastingPerformance. In terms of point accuracy (MAE and RMSE), MS-STDT exhibits a significant performance margin over both graph-based and grid-based baselines.

Graph-Structured Data (PeMS04/07/08): Our model effectively captures the complex topology of traffic networks.

Method NYCTaxi T-Drive CHIBike MAE↓

RMSE↓

CRPS↓

MAE↓

RMSE↓

CRPS↓

MAE↓

RMSE↓

CRPS↓

TimeGrad

14.990±0.168 24.484±0.229 0.38±0.097 19.826±0.170 35.471±0.397 0.43±0.016 4.074±0.132

5.876±0.221 0.58±0.118

D3VAE

13.745±0.154 22.179±0.277 0.86±0.160 18.791±0.149 33.876±0.285 0.84±0.375 4.061±0.130

5.818±0.159 0.53±0.040

MG-TSD

12.446±0.138 21.365±0.216 0.37±0.178 16.562±0.123 32.092±0.242 0.44±0.116 3.893±0.109

5.456±0.126 0.40±0.163

DiffSTG

13.464±0.148 22.145±0.201 0.42±0.094 17.647±0.181 32.417±0.255 0.37±0.086 4.013±0.100

5.362±0.108 0.39±0.121

USTD

12.132±0.150 21.103±0.239 0.36±0.067 16.214±0.104 31.766±0.211 0.35±0.126 3.899±0.117

5.473±0.156 *0.34±0.097

UrbanDiT

*10.169±0.140 18.019±0.223 *0.33±0.174 *14.623±0.129 *29.812±0.219 *0.34±0.161 *3.698±0.101 *5.357±0.124 0.36±0.122

ST-SSL

13.054±0.014 22.821±0.027

-

19.191±0.019 34.772±0.025

-

4.054±0.005

5.820±0.007

-

UniST

10.291±0.022 17.937±0.032

-

15.173±0.017 30.237±0.024

-

3.879±0.006

5.426±0.009

-

STD-MAE

12.411±0.010 20.813±0.019

-

17.184±0.015 32.143±0.026

-

3.903±0.009

5.586±0.018

-

BasisFormer

11.426±0.010 18.536±0.029

-

16.293±0.013 31.098±0.027

-

3.993±0.009

5.586±0.026

-

TimeMixer

11.327±0.013 18.693±0.027

-

16.119±0.019 30.972±0.025

-

3.761±0.012

5.431±0.023

-

STDN

10.216±0.003 *17.921±0.011

-

15.010±0.002 29.994±0.021

-

3.816±0.001

5.446±0.003

-

MS-STDT(Ours) 9.132±0.122 16.627±0.181 0.26±0.088 12.681±0.134 27.053±0.196 0.30±0.038 3.347±0.080

5.041±0.102 0.33±0.075

Table 2: Performance comparison of MAE, RMSE, and CRPS on six datasets. Best results are bolded, second-best are marked with *.

On the PeMS08 dataset, for instance, MS-STDT achieves an MAE of 10.391, representing a reduction of 13.1% compared to the strongest diffusion baseline, UrbanDiT (11.962), and 13.4% compared to the advanced transformer STDN (12.003). This indicates that our multi-scale guidance strategy allows the model to retain fine-grained spatial dependencies that standard graph diffusion often smooths over.

Grid-Based Data (NYC, T-Drive, CHIBike): The superiority of MS-STDT extends to grid-based inputs, demonstrating its versatility. On the highly dynamic T-Drive dataset, we surpass the second-best method (UrbanDiT) by reducing the MAE from 14.623 to 12.681 (↓13.3%). Notably, while non-generative baselines like UniST and TimeMixer perform competitively on simpler metrics, they struggle to match the peak performance of MS-STDT on high-variance datasets (e.g., NYCTaxi), confirming the necessity of our guided generative approach.

Probabilistic Forecasting Quality. Beyond simple accuracy, the CRPS metric reveals the model's ability to model the full distribution of traffic states. As shown in Table 2, MS-STDT achieves the lowest CRPS across all scenarios. On PeMS04, our model reduces CRPS to 0.30, significantly outperforming the standard diffusion baseline DiffSTG (0.42). This suggests that the Guided Diffusion Process Module (GDPM) does not merely memorize the mean trajectory but accurately calibrates the predictive uncertainty, producing tighter and more reliable confidence intervals-a critical attribute for safety-critical ITS applications.

Comparative Analysis. Comparing across categories, we observe that while self-supervised methods (e.g., UniST, STD-MAE) offer strong stability, they often lack the granular resolution provided by generative models. Conversely, standard diffusion models (e.g., TimeGrad, MG-TSD) often suffer from stochastic instability, leading to higher RMSE. MSSTDT effectively bridges this gap: by anchoring the diffusion process with coarse-scale guidance, it combines the stability of deterministic encoders with the generative expressiveness of diffusion.

4.3 Ablation Study

To validate the contribution of each component, we conducted ablation experiments across all six datasets (Table 3). The removal of the Guided Diffusion Process Module (w/o GDPM) resulted in the most significant performance degradation, confirming its pivotal role in stabilizing generation via multi-scale supervision. Similarly, excluding the Multi-Scale Fusion (w/o MSFO) or Multi-Scale Sampling (w/o MSS) consistently impaired accuracy, verifying that both hierarchical feature extraction and adaptive cross-scale aggregation are essential for capturing complex dependencies. Furthermore, the performance drop in w/o SMA highlights the necessity of explicit spatial modeling. Finally, replacing our decoupled attention with a unified variant (w/ STMA) yielded inferior results, supporting the design choice of separating spatial and temporal processing for more precise feature learning.

4.4 Effect of Parameters

We further investigate the impact of two critical parameters on model performance: the number of diffusion steps and the masking ratio used in training. Specifically, we varied the diffusion step from 20 to 100 and the masking ratio from 0.05 to 0.25, evaluating their effects on MAE across benchmark datasets. The results reveal that model accuracy generally improves with an increased diffusion step up to an optimal point, beyond which performance degrades due to potential over-smoothing. Similarly, a moderate masking ratio yields the best results, suggesting a balance between model robustness and information retention. These findings underscore the importance of careful hyperparameter tuning for optimal spatial-temporal forecasting performance.

4.5 Robustness and Efficiency Analysis

Zero-Shot Resilience. We evaluated model resilience against sensor failures by testing on data with 0-30% random missing rates without retraining. As shown in Fig. 4(a), MS-STDT demonstrates superior stability compared to baselines. While the deterministic STDN degrades rapidly (MAE rising from ∼18 to >24) and generative models like UniST and UrbanDiT exhibit linear error increases, MS-STDT maintains a significantly flatter degradation curve. Notably, at 30% sparsity, our model matches the performance of baselines at only 010% missing rates, validating the Spatial-Temporal Process Module's ability to impute missing global context.

Computational Efficiency. Fig. 4(b) details the computational overhead. Despite its multi-scale architecture, MSSTDT achieves a highly favorable efficiency trade-off. It requires only ∼83 ms/iter for training, significantly faster than UrbanDiT (∼730 ms) and comparable to lightweight baselines due to our parallelized encoder. Inference is similarly accelerated (∼908 ms/iter vs. ∼2046 ms for UrbanDiT) via our guided diffusion strategy. Furthermore, MS-STDT maintains a moderate memory footprint (∼7303 MB), 21% lower than competitive diffusion models, ensuring deployment feasibility.

5 RelatedWork

Diffusion Models for Traffic Flow Forecasting. Diffusion models have become an important paradigm for traf-

(a)

24

MAE

22

20

18

MS-STDT

UrbanDiT

UniST

STDN

0

10

20

30

Missing Rate (%)

UrbanDiT Ours

Figure 4: Robustness (a) and Efficiency (b) Analysis.

fic forecasting due to their ability to model complex predictive distributions and uncertainty [Zhang et al., 2021; R¨uhling Cachay et al., 2023; Wen et al., 2023; Hu et al., 2024a]. Early work such as TimeGrad [Rasul et al., 2021] introduced autoregressive denoising for temporal modeling, while DiffSTG [Wen et al., 2023] further incorporated graph structure into diffusion-based forecasting. More recent studies have explored generation stability and scalability, e.g., MG-TSD [Fan et al., 2024] via multi-granularity guidance and UrbanDiT [Yuan et al., 2025] via Diffusion Transformers. However, most existing methods still treat diffusion as a largely monolithic denoising process. In contrast, MSSTDT explicitly aligns the reverse process with the intrinsic coarse-to-fine hierarchy of traffic data, using stable coarsescale trends to guide fine-grained generation.

Transformers for Traffic FlowForecasting. Transformers dominate long-range spatial-temporal modeling [Wu et al., 2021; Jiang et al., 2023; Jin et al., 2023]. Recent advancements have increasingly focused on pattern disentanglement and generalization. For instance, STDN [Cao et al., 2025] proposes a decomposition network to separate traffic data into distinct trend and seasonality components, and UniST [Yuan et al., 2024] utilizes masked pre-training to learn robust representations for cross-city transfer. However, while architectures like STDN excel at isolating deterministic macrotrends, they often lack the probabilistic capacity to model the stochastic uncertainty inherent in dynamic traffic flows. MS-STDT addresses this limitation by synthesizing the structural decomposition benefits of these Transformers with the generative expressiveness of diffusion models, unifying them within a hierarchical multi-scale framework that is both physically consistent and computationally efficient.

6 Conclusion

In this paper, we proposed the Coarse-to-Fine Latent Guidance strategy via MS-STDT to address the challenge of multi-scale traffic heterogeneity. By reformulating diffusion as a hierarchical generative process, our method utilizes intrinsic data structures as structural anchors to stabilize prediction without external labels. Extensive experiments confirm that MS-STDT consistently outperforms existing baselines in accuracy while demonstrating superior zero-shot robustness and computational efficiency. In future work, we plan to explore its applicability to broader spatial-temporal domains [Lian et al., 2026].

Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Nos.T2293771 and 42361144718). The funders had no role in the study design, data collection, analysis, decision to publish, or preparation of the manuscript.