SeisDiff-denoNIA: Diffusion Seismic Denoising

• SeisDiff-denoNIA is a diffusion-based seismic denoising method that uses DDPM, time-conditioned U-Nets, and reverse sampling to suppress noise in seismic images.
• It is applied in various settings, including VSP, to attenuate tube-wave and field noise while preserving essential reflected body-wave signals.
• The approach adapts training regimes from synthetic noisy-clean pairs to direct field-noise modeling, achieving significant improvements in SSIM and SNR.

SeisDiff-denoNIA is a diffusion-based seismic denoising designation used in several recent seismic-processing contexts built around denoising diffusion probabilistic models, time-conditioned U-Nets, and reverse-time sampling for noise suppression on seismic images, shot gathers, or VSP acquisitions. In its most specific 2025 VSP usage, it denotes the Seismic Diffusion Model for Denoising applied to tube-wave attenuation in vertical seismic profiling data, where a conditional DDPM learns to remove coherent tube-wave noise while preserving reflected body-wave events (Zhu et al., 1 Mar 2025). Earlier and parallel uses describe a seismic denoising variant trained on synthetic noisy-clean patches (Durall et al., 2022) and a later reformulation that trains directly on extracted field noise rather than clean signal labels (Zhu et al., 3 Sep 2025).

1. Terminology and scope

In the supplied literature, the label “SeisDiff-denoNIA” does not denote a single immutable implementation. Rather, it refers to a closely related set of diffusion-based denoising formulations in seismic processing, all grounded in DDPM-style forward noising, learned reverse denoising, and U-Net backbones. The most coherent line of usage runs from the 2022 seismic denoising variant in “Deep Diffusion Models for Seismic Processing” through the 2025 VSP tube-wave attenuation framework “SeisDiff-deno,” and then to the 2025 “NoiseNoise is All You Need” formulation that rethinks denoising by modeling field noise directly (Durall et al., 2022, Zhu et al., 1 Mar 2025, Zhu et al., 3 Sep 2025).

Source	Problem setting	Distinguishing feature
(Durall et al., 2022)	Seismic denoising on BP 1994 and Model94 patches	Standard image DDPM with time-conditional U-net
(Zhu et al., 1 Mar 2025)	Tube-wave attenuation in VSP and DAS-VSP shot-gathers	Conditional DDPM with contaminated gather conditioning and fast DDIM sampling
(Zhu et al., 3 Sep 2025)	DAS-VSP denoising trained directly on field noise	Noise-target training with denoised shot = noisy shot – predicted noise

The supplied summaries also reuse the label in descriptions of interpolation and Newtonian-noise contexts (Wei et al., 2023, Ophardt et al., 15 Dec 2025, Chen et al., 9 Jan 2026). This suggests that “SeisDiff-denoNIA” is not a fully standardized bibliographic name across secondary summaries, whereas the denoising usage is the most consistent technical meaning within the seismic-processing material.

2. Seismic problem class and operational motivation

The denoising problem addressed by SeisDiff-denoNIA depends on the acquisition setting. In the general seismic-denoising variant, the objective is attenuation of undesired incoherent or Gaussian-like noise on 2-D seismic images or gathers. In the VSP-specific formulation, the target is tube-wave attenuation in vertical seismic profiles, where tube waves are guided waves traveling along the fluid–solid interface of the borehole and may arrive long before reflected body waves with amplitudes that overwhelm the reflections of interest (Durall et al., 2022, Zhu et al., 1 Mar 2025).

The VSP motivation is operationally specific. When the well is under active production or injection, tube waves can mask shallow reflections, reduce signal-to-noise ratio, and force interpreters to use only late arrivals at large source-receiver offsets. Modern fiber-optic DAS-VSP runs in real time during production, so tube waves are particularly strong. Suppressing them without distorting genuine reflections is therefore critical for continuous reservoir monitoring, fracture characterization, and cost-effective seismic acquisition (Zhu et al., 1 Mar 2025).

The 2025 field-noise formulation reframes the same broad denoising objective. Instead of treating clean seismic signal as the primary target distribution, it treats real field noise as the training target. The stated rationale is that real noise distributions, including tube waves, coupling noise, fading noise, and environmental noise, exhibit complex, field-specific statistics that synthetic labels cannot replicate. The corresponding denoising rule is explicit: denoised shot = noisy shot – predicted noise (Zhu et al., 3 Sep 2025).

3. Probabilistic formulation

Across its denoising variants, SeisDiff-denoNIA adopts the canonical diffusion decomposition into a forward Gaussian noising process and a learned reverse denoising process. For clean seismic data $x_0$, the forward process is written as

$$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$

with $\alpha_t=1-\beta_t$ and $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$. Marginalizing intermediate states yields

$$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$

so that

$$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$

In the VSP tube-wave framework, the reverse model is conditional: a neural network $\varepsilon_\theta(x_t,c,t)$ predicts the noise component at timestep $t$, conditioned on the contaminated shot-gather $c$, and training minimizes the simple noise-prediction loss

$$\mathcal{L}_t=\mathbb{E}_{x_0,\varepsilon,c}\Bigl[\bigl\|\varepsilon-\varepsilon_\theta(\sqrt{\bar\alpha_t}x_0+\sqrt{1-\bar\alpha_t}\varepsilon,c,t)\bigr\|_2^2\Bigr].$$

The full objective is $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$0 (Zhu et al., 1 Mar 2025).

The 2022 denoising variant uses the standard DDPM parameterization $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$1, with learning formulated as expected $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$2 error in the predicted noise and a linear $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$3 schedule over $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$4 steps (Durall et al., 2022). The 2025 field-noise formulation preserves the same diffusion formalism but changes the data distribution: $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$5 is sampled from the field-noise distribution, and the model learns $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$6 rather than a clean-seismic distribution (Zhu et al., 3 Sep 2025).

Noise scheduling differentiates the variants. The 2022 formulation uses a linear schedule with $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$7, $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$8, and $$q(x_t \mid x_{t-1})=\mathcal{N}\bigl(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t \mathbf{I}\bigr),$$9 (Durall et al., 2022). The VSP tube-wave framework instead uses a cosine schedule

$\alpha_t=1-\beta_t$0

with small offset $\alpha_t=1-\beta_t$1, explicitly to preserve more signal in early steps (Zhu et al., 1 Mar 2025).

4. Network architecture and inference mechanics

The architectural core in the VSP formulation is a conditional DDPM with a 2D U-Net backbone enhanced by ResNet blocks and self-attention, together with a fast DDIM sampler at inference time. The input comprises two concatenated channels—the contaminated shot-gather $\alpha_t=1-\beta_t$2 and the current noisy latent $\alpha_t=1-\beta_t$3—and the output is a single-channel prediction of $\alpha_t=1-\beta_t$4. The U-Net has five resolutions in downsampling and upsampling paths; each resolution uses 2–4 ResNet blocks with GroupNorm, Swish, convolution, dropout, and convolution; self-attention layers are inserted at user-specified resolutions; and skip connections concatenate encoder feature maps to the decoder. Timestep conditioning is implemented through a sinusoidal positional encoding of $\alpha_t=1-\beta_t$5, injected into each ResNet block via FiLM or addition (Zhu et al., 1 Mar 2025).

The implementation summary for the VSP model reports the following key hyper-parameters: input/output channels $\alpha_t=1-\beta_t$6, base filters $\alpha_t=1-\beta_t$7 with multipliers $\alpha_t=1-\beta_t$8, number of ResBlocks per level $\alpha_t=1-\beta_t$9, attention at the lowest two resolutions, and dropout $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$0 (Zhu et al., 1 Mar 2025).

The earlier 2022 denoising variant uses the time-conditional U-net backbone of Ho et al. (2020): four down-sampling levels of residual blocks plus convolutions, a bottleneck with one self-attention layer, four up-sampling levels, skip connections, and sinusoidal or learned timestep embeddings. All convolutions are $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$1, and channel widths start at 128 and double on each downsample (Durall et al., 2022). The later field-noise formulation preserves the same broad design logic but states the conditioning more explicitly: a noisy seismic shot with real field noise is concatenated or cross-injected at each U-Net level to guide the denoiser, with residual blocks and self-attention modules at selected resolutions (Zhu et al., 3 Sep 2025).

Inference speed is a major design axis. In the VSP tube-wave model, a deterministic DDIM sampler with $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$2 is used, specifically $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$3 versus $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$4, and $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$5 is chosen to produce identical outputs under identical conditions (Zhu et al., 1 Mar 2025). The field-noise formulation instead reports accelerated sampling with DPM-Solver, reducing steps from 1000 reverse steps to approximately 20–50 with negligible quality loss (Zhu et al., 3 Sep 2025). This suggests a progression from standard DDPM sampling, to DDIM acceleration, to ODE-based solver acceleration as the denoising line matures.

5. Data construction and training regimes

The training regime changes substantially across the three denoising formulations, and those changes encode different assumptions about what should be learned.

The 2022 variant trains on the BP 1994 dataset by extracting random $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$6 or $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$7 patches, ensuring that no patch has more than $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$8 zeros, and synthetically adding Gaussian noise whose variance is drawn so that the added noise energy is $\bar{\alpha}_t=\prod_{i=1}^t \alpha_i$9 of the patch’s energy. Training uses batch size 32, a linear $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$0 schedule, $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$1, and 200,000 iterations, with standard per-patch zero mean/unit variance scaling and no further pre-conditioning or normalization (Durall et al., 2022).

The 2025 VSP tube-wave framework uses paired noisy-clean supervision. For synthetic VSP data, the SEAM Phase I elastic model generates noise-free shot-gathers, and linear noise is simulated and superposed as upward and downward events. For field DAS-VSP, clean “shut-in” recordings have no tube waves, and simulated linear tube-wave noise is added to form paired $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$2 data. Optimization uses AdamW, learning rate $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$3, batch size 16, 20,000 total iterations, EMA rate 0.999, diffusion timesteps $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$4, and DDIM sampling $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$5 (Zhu et al., 1 Mar 2025).

The 2025 field-noise version eliminates clean labels. From each field DAS-VSP gather $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$6, the first-arrival time $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$7 is identified, and a pure noise segment $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$8 for $$q(x_t\mid x_0)=\mathcal{N}\bigl(x_t;\sqrt{\bar\alpha_t}\,x_0,(1-\bar\alpha_t)\mathbf{I}\bigr),$$9 is extracted. A $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$0 patch window is slid across these prestack noise segments, producing approximately 16,000 patches from 800 shots, followed by random cropping and amplitude normalization. The reported source is Gulf-of-Mexico deepwater 4D DAS-VSP from 2015–2018, with strong tube waves during injection as well as coupling noise and fading noise. Training uses PyTorch on A100 (40 GB), AdamW, learning rate $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$1, batch size 16, and 300–500 epochs to convergence (Zhu et al., 3 Sep 2025).

These regimes correspond to three distinct supervisory philosophies: synthetic signal-plus-noise pairs, contaminated-to-clean conditional VSP learning, and direct field-noise modeling. A plausible implication is that the name SeisDiff-denoNIA tracks a methodological lineage more than a single frozen data protocol.

6. Empirical behavior, computational profile, and limitations

The VSP tube-wave framework reports strong gains relative to an FK-filter baseline on synthetic SEAM data with simulated tube waves. The FK filter yields SSIM $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$2 and SNR $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$3 dB, whereas SeisDiff-deno yields SSIM $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$4 and SNR $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$5 dB. In a generalization test where Gulf of Mexico 4D DAS-VSP field noise is added to SEAM gathers, the FK filter gives correlation coefficient $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$6 and SNR $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$7 dB, while SeisDiff-deno gives correlation coefficient $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$8 and SNR $$x_t=\sqrt{\bar\alpha_t}\,x_0+\sqrt{1-\bar\alpha_t}\,\varepsilon,\qquad \varepsilon\sim\mathcal N(0,\mathbf I).$$9 dB; the accompanying figures are described as showing that SeisDiff-deno removes tube-wave coherency while preserving reflections more effectively (Zhu et al., 1 Mar 2025).

Its computational profile is explicitly practical. Training on NVIDIA A100 GPUs takes approximately 20,000 iterations in a few days. Inference uses a single NVIDIA RTX A4000 with 16 GB at 50 DDIM steps. For a $\varepsilon_\theta(x_t,c,t)$0 shot-gather, 50 steps take on the order of a few seconds, and the throughput scales to hundreds of shot-gathers per hour on a single GPU, with memory footprint fitting within 16 GB GPU memory (Zhu et al., 1 Mar 2025).

The 2022 variant reports mean $\varepsilon_\theta(x_t,c,t)$1 standard deviation over 500 random patches. On held-out BP ’94 patches, SeisDiff-denoNIA attains SSIM $\varepsilon_\theta(x_t,c,t)$2 and SNR $\varepsilon_\theta(x_t,c,t)$3 dB $\varepsilon_\theta(x_t,c,t)$4 dB, versus FX-Decon at SSIM $\varepsilon_\theta(x_t,c,t)$5 and SNR $\varepsilon_\theta(x_t,c,t)$6 dB $\varepsilon_\theta(x_t,c,t)$7 dB. On the out-of-distribution Model94 dataset, however, SeisDiff-denoNIA drops to SSIM $\varepsilon_\theta(x_t,c,t)$8 and SNR $\varepsilon_\theta(x_t,c,t)$9 dB $t$0 dB, while FX-Decon reports SSIM $t$1 and SNR $t$2 dB $t$3 dB. The qualitative description states that diffusion removes more random noise but occasionally attenuates weak coherent arrivals, whereas FX-Decon leaves some residual grain but preserves all primaries (Durall et al., 2022).

The field-noise formulation emphasizes low-SNR robustness rather than only paired-clean reconstruction. Its synthetic ablation reports that at high SNR both models recover signal, but below $t$4 dB the Train-on-Noise formulation retains finer reflector detail. Table 1 gives cross-correlation and RMSE versus SNR; at $t$5 dB, Train-on-Seismic has CC $t$6 and RMSE $t$7, while Seismic-Perturbed has CC $t$8 and RMSE $t$9. The stated statistical finding is that Train-on-Noise outperforms Train-on-Seismic by approximately $c$0–$c$1 CC at $c$2 dB and reduces RMSE by approximately $c$3–$c$4 (Zhu et al., 3 Sep 2025).

Limitations are reported in all variants. The 2022 model has limited generalization across geologies and acquisition styles, with a drop in SSIM/SNR on Model94, and in some cases weak coherent events are misclassified as noise (Durall et al., 2022). The field-noise model notes that converted-wave preservation depends on its presence in training noise segments; if a noise segment overlaps a faint converted phase, it could be partially learned as “noise,” and simplistic perturbations slightly degrade performance (Zhu et al., 3 Sep 2025). In the VSP setting, the central technical tension remains the same: suppress coherent tube-wave energy without distorting genuine reflections (Zhu et al., 1 Mar 2025).

Taken together, SeisDiff-denoNIA denotes an evolving diffusion-denoising lineage in seismic processing. Its common core is the replacement of fixed linear suppression rules by a learned stochastic model of seismic or noise distributions; its main internal divergence lies in what is modeled directly—clean seismic signal, contaminated-to-clean conditional mapping, or field noise itself.