DS-Diffusion: Style-Guided Time-Series Generation

• The paper demonstrates that DS-Diffusion enhances time-series generation by steering denoising with explicit STL-derived trend and seasonal styles.
• It employs a frozen EDM backbone combined with style-guided kernels and a time-information based hierarchical denoising mechanism to separate low- and high-frequency details.
• Empirical results show up to 94% reduction in divergence metrics and improved alignment with real data, validating its effectiveness and interpretability.

Searching arXiv for the specified paper and closely related diffusion/style-guidance work to ground the article. DS-Diffusion is a time-series generation framework that augments a diffusion backbone with explicit data-style guidance, using style components extracted from real sequences to steer generation without retraining the base diffusion model. In the formulation introduced in "DS-Diffusion: Data Style-Guided Diffusion Model for Time-Series Generation," the backbone is an EDM/ImagenTime-style model trained once on image-transformed time series, while inference is refined by style-guided kernels and a time-information based hierarchical denoising mechanism (THD). The stated objectives are to avoid retraining for new conditions, reduce distributional bias between generated and real data, and make the inference path more interpretable by tying generated samples to identifiable source styles (Sun et al., 23 Sep 2025).

1. Problem setting and the definition of data style

The method is motivated by three limitations attributed to existing diffusion models for time-series generation. First, conditional guidance typically requires retraining the whole diffusion model or training extra classifiers or guidance networks when new conditions are introduced. Second, generated sequences can exhibit a bias relative to the real data distribution, which can propagate to downstream forecasting, classification, or anomaly detection tasks. Third, the denoising process is ordinarily difficult to interpret because it proceeds in a high-dimensional latent space and does not explicitly reveal which real-data styles underlie a generated sample (Sun et al., 23 Sep 2025).

Time-series generation is formulated as learning a real-data distribution and sampling new sequences that preserve trends, seasonality, and correlations while increasing quantity and diversity. DS-Diffusion treats “data style” as structural components of a time series extracted by STL decomposition. For a sample $x_i \in \mathbb{R}^{l \times F}$ from a dataset

$$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$

the style extraction function $\Phi$ is defined as

$$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$

where $S_{\text{tr}}$ is the trend component and $S_{\text{seas}}$ is the seasonal component. The trend is the long-term, low-frequency movement of the sequence, and the seasonal component is the periodic, high-frequency fluctuation within specific periods. These components are then reused as explicit conditions for generation (Sun et al., 23 Sep 2025).

This definition is narrower than a generic notion of “style” in other generative settings. In DS-Diffusion, style is not an abstract label or a learned latent without direct semantics; it is specifically the pair of STL-derived structural components that capture the core distributional structure of a time series. A common misconception is therefore to treat DS-Diffusion as a standard class-conditional diffusion model. Its conditioning signal is instead a decomposition-derived representation of real temporal structure (Sun et al., 23 Sep 2025).

2. Core architecture and frozen-backbone conditioning

DS-Diffusion consists of three parts: a base diffusion model, style-guided kernels, and THD implemented through transformers inside those kernels. The base model is an EDM backbone as used in ImagenTime, operating on time series represented as images. Sampling begins from Gaussian noise,

$x_T \sim \mathcal{N}(0, I),$

and the denoising network $\Upsilon$ predicts the gradient of the log-likelihood at each timestep:

$\nabla_{x_t} \log p_t(x_t) = \Upsilon(x_t, t).$

Training uses the standard diffusion noise-prediction objective

$$\mathcal{L} = \mathbb{E}_{t, x_0, \epsilon} \left[ \left\| \epsilon - \epsilon_\theta(x_t, t) \right\|^2 \right],$$

and the reverse process is written as

$$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$0

This yields the usual EDM denoising trajectory from $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$1 to $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$2 (Sun et al., 23 Sep 2025).

The architectural novelty lies in what happens after each backbone denoising step. DS-Diffusion applies a style-guided kernel $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$3,

$$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$4

where $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$5 denotes the extracted data styles $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$6. The kernel refines the current sample using THD, adjusting low- and high-frequency components according to the supplied style. The EDM backbone remains frozen during inference; only the style-guided kernel contains learnable parameters, and those parameters are trained once. New styles are introduced by changing the style input $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$7, not by updating the diffusion backbone (Sun et al., 23 Sep 2025).

This separation between unconditional denoising and externalized conditioning is the principal design decision of the framework. Rather than embedding conditions directly into the diffusion network, DS-Diffusion places style control in a superimposed operator that acts on the denoising trajectory. The paper presents this as the reason the method can adapt to new styles without retraining the backbone (Sun et al., 23 Sep 2025).

3. Style-guided kernels and time-information based hierarchical denoising

A style-guided kernel is defined as an operator that transforms the current sample using the timestep $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$8, the extracted styles $$D_{L \times F} = \{x_1^{l \times F}, x_2^{l \times F}, \dots, x_n^{l \times F}\},$$9, and a decomposition of the current sample into trend, seasonal, and residual components. Its internal mechanism is THD, which first maps the current latent back into time-series form, decomposes it, applies guided reconstruction to the structured components, and then re-encodes the result into the latent or image domain (Sun et al., 23 Sep 2025).

At each denoising step, the latent is first inverted through the image transform:

$\Phi$0

STL decomposition is then applied to obtain

$\Phi$1

where $\Phi$2 is the inferred low-frequency trend, $\Phi$3 is the inferred seasonal component, and $\Phi$4 is the residual component. Two transformers are then used for guided denoising:

$\Phi$5

$\Phi$6

The updated series is reconstructed as

$\Phi$7

and transformed back:

$\Phi$8

The residual $\Phi$9 is preserved rather than denoised away, which the authors describe as a way to retain stochasticity and avoid over-smoothing, especially in high-frequency components (Sun et al., 23 Sep 2025).

THD is explicitly hierarchical in frequency space. The paper reports a Fourier-analysis-based observation that early denoising steps are dominated by clearer low-frequency structure, whereas later steps make high-frequency detail more reliable. Accordingly, DS-Diffusion emphasizes trend guidance in early steps and seasonal guidance in later steps. The intended effect is to construct a realistic outline first and then refine periodic detail. This division of labor is presented as a mechanism for reducing interference between low- and high-frequency reconstruction and thereby narrowing the gap between generated and real distributions (Sun et al., 23 Sep 2025).

The same mechanism also underpins interpretability. Because the denoising path is decomposed into explicit trend, seasonal, and residual channels, one can inspect how the generated sample is being aligned with a selected real-data style at each step. The framework therefore makes style influence visible at the component level rather than leaving it implicit in a monolithic latent trajectory (Sun et al., 23 Sep 2025).

4. Training procedure, conditional use, and interpretability claims

The training procedure has two stages. The EDM/ImagenTime base diffusion model is trained on image-transformed time series with a U-Net backbone, AdamW, 18 sampling steps, and 1000 epochs. Separately, the two THD transformers, $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$0 and $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$1, are trained with Adam and learning rate $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$2. Their inputs are the current decomposed component, the corresponding style component, and the timestep $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$3; embedding layers map these signals into high-dimensional representations, and multi-head self-attention is used to capture dependencies across time (Sun et al., 23 Sep 2025).

The paper does not explicitly provide a THD loss formula. Instead, the role of the transformers is inferred from the structure of the model and the empirical outcomes: they learn to produce guided trend and seasonal components that, when recombined, yield samples whose distribution is closer to the real data distribution. This suggests that THD is functionally trained as a denoising-and-alignment module layered on top of the frozen diffusion process rather than as an independent generative model (Sun et al., 23 Sep 2025).

Conditional generation is straightforward once the model is trained. A practitioner selects a real sequence or a style prototype, applies STL to obtain $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$4, samples $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$5, and runs the frozen EDM denoising process while applying the style-guided kernel at each step. Because the condition is carried entirely by the style input, new styles can be introduced without modifying diffusion weights. The paper describes this workflow as enhancing flexibility and adaptability to specific conditions (Sun et al., 23 Sep 2025).

The interpretability claim is similarly grounded in explicit style provenance. Each generated sample is associated with a specific pair of style components extracted from real data, so the origin style is known. The paper states that generated samples can clearly indicate the data style from which they originate, and supports that claim with PCA, t-SNE, and density-plot evidence showing that DS-Diffusion samples cluster closer to real data than ImagenTime and that their probability density functions more closely track real PDFs. At the same time, the authors note that the paper does not define a dedicated interpretability score; interpretability is instead argued from the decomposed inference process and the style-tracking behavior of the generated samples (Sun et al., 23 Sep 2025).

5. Evaluation, metrics, and empirical findings

The empirical study uses four multivariate datasets: Stocks, consisting of Google daily stock data with six variables; Energy, a 28-variable appliance energy consumption dataset; MuJoCo, a 14-variable simulated robotics dataset; and Sine, a five-variable synthetic dataset with clear trend and periodicity. DS-Diffusion is compared against 11 baselines: ImagenTime, KoVAE, DiffTime, GT-GAN, TimeGAN, RCGAN, C-RNN-GAN, T-Forcing, P-Forcing, WaveNet, WaveGAN, and LS4 (Sun et al., 23 Sep 2025).

The primary quantitative metrics are the predictive score and discriminative score adopted from ImagenTime. The predictive score evaluates how generated data behaves in forecasting tasks, with lower values indicating greater similarity to real data. The discriminative score measures how easily a discriminator can separate real and generated sequences; lower values indicate smaller distributional bias. On the real-world datasets Stocks, Energy, and MuJoCo, DS-Diffusion achieves an average 5.56% decrease in predictive score and an average 61.55% decrease in discriminative score relative to ImagenTime. On Sine, the corresponding reductions are 7.09% and 94.42% (Sun et al., 23 Sep 2025).

The paper further evaluates distributional alignment through KL divergence, JS divergence, Wasserstein distance, and the Kolmogorov–Smirnov statistic. Average reductions across datasets are reported as 5.94% for KL divergence, 74.14% for JS divergence, 96.37% for Wasserstein distance, and 88.12% for KS. These results are presented as evidence that DS-Diffusion brings the generated distribution closer to the real distribution in multiple statistical senses, not merely according to a discriminator-based metric (Sun et al., 23 Sep 2025).

Ablation studies address three design choices: the decomposition method, the sequence model inside THD, and the contribution of the two THD transformers. STL consistently outperforms Fourier Transform, Continuous Wavelet Transform, and time-domain gradients, especially on non-ideal real-world datasets, although Fourier Transform can match STL on perfectly periodic synthetic data. Transformers outperform GRU and MLP alternatives, which produce higher predictive and discriminative scores. The trend transformer is particularly important: on MuJoCo, removing $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$6 raises the discriminative score from 0.005 to 0.225, whereas removing $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$7 increases it to 0.017. The paper interprets this as showing that $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$8 establishes realistic sequence profiles while $$S = \Phi(x_i^{l \times F}), \quad S = (S_{\text{tr}}, S_{\text{seas}}),$$9 refines periodic detail and style consistency (Sun et al., 23 Sep 2025).

The additional control afforded by THD is not free. DS-Diffusion uses more parameters because of the extra transformers, with totals reported at roughly 4.8M–6.6M versus about 2M for ImagenTime on certain datasets, and wall-clock training time rises modestly, for example from 1h10m to 1h24m on Stocks. The authors describe this as an acceptable increase given the improvements in generation quality, distributional alignment, and style control (Sun et al., 23 Sep 2025).

6. Conceptual position, related work, limitations, and uses

Within time-series diffusion, DS-Diffusion is positioned against both unconditional image-transformed generators such as ImagenTime and conditional approaches that integrate conditions directly into the diffusion network or loss. The paper names Diffusion-TS, FIDE, and MG-TSD as examples of methods that typically require retraining or architectural modification for new conditions. By contrast, DS-Diffusion casts data style as the pair of trend and seasonality components extracted by STL and externalizes conditioning into a style-guided kernel applied to a frozen backbone. This suggests a plug-and-play interpretation of conditioning in which the condition is not fused into the denoiser itself but injected as a separate operator over the denoising trajectory (Sun et al., 23 Sep 2025).

The broader literature shows that this idea of style-guided diffusion has analogues in other modalities, but with different notions of style and different conditioning mechanisms. DiffTSST applies content and style encoders with classifier-free guidance for time-series style transfer (Nagda et al., 13 Oct 2025). ParaGuide uses paraphrase-conditioned diffusion with plug-and-play gradient guidance for textual style transfer (Horvitz et al., 2023). SGDiff adds an image-based style encoder and multi-condition classifier-free guidance for fashion synthesis (Sun et al., 2023). DiffuseST performs training-free image style transfer through separated content and style injection across diffusion steps (Hu et al., 2024). Diffusion-based language modeling for StylePTB uses style tokens to control fine-grained textual transformations (Lyu et al., 2023). PrivDiffuser guides sensor-data diffusion with positive public-attribute and negative private-attribute signals, together with mutual-information regularization (Yang et al., 2024). These works do not redefine DS-Diffusion itself, but they situate it within a larger research program in which diffusion trajectories are steered by data-derived structural or stylistic signals rather than by unconditional sampling alone.

The limitations noted for DS-Diffusion are concrete. The model size and training time increase because of the transformers inside THD. The framework is currently grounded in image-transformed time-series representations rather than direct multi-frequency sequence representations. Future work identified by the authors includes more efficient style extraction methods, model structure optimization, knowledge distillation, and extensions to domains such as agriculture and healthcare, including sensor, olfactory, and blood glucose data (Sun et al., 23 Sep 2025).

The practical use cases emphasized by the paper are style-controlled generation, low-bias synthetic augmentation, and interpretable conditional sampling. The examples given include financial regimes such as bullish or bearish stock behavior, seasonal energy-usage profiles, blood glucose or vital-sign trajectories in healthcare, sensor readings for industrial or IoT applications, and climate or weather series with specified long-term and seasonal patterns. In those settings, the value of DS-Diffusion lies not only in generating realistic sequences, but in generating sequences whose trend and seasonality can be traced to explicit real-data style sources while avoiding the need to retrain the diffusion model for each new condition (Sun et al., 23 Sep 2025).