DSN-RD: Domain-Statistics-Driven Residual Diffusion for Data-Efficient, Compute-Aware Super-Resolution in Frequency-Shifted Imagery

DSN-RD: Domain-Statistics-Driven Residual Diffusion for Data-Efficient, Compute-Aware Super-Resolution in Frequency-Shifted Imagery

C. Kowsika T. Kaaviya Varshini, Sajana Parveen, Annanya R K Mr. N. Ravi, Mrs. G. Aishwaryalakshini

Abstract – Diffusion models are well-suited for image super-resolution (SR), but suffer from challenges in domains with non-natural image frequency statistics, limited paired training data, and limited sampling budget. Adversarial methods can handle some of these conditions, but can suffer from instability during training and augmentation dependence. We introduce DSN-RD, a conditional residual-diffusion image super-resolution method built with the following insight: compute only a few domain statistics once and use them in three ways: (1) as domain shift and data scarcity prior for the diffusion model (radially averaged residual frequency spectrum), (2) as a mechanism to avoid spurious detail in flat regions (stability without a discriminator), and (3) as a sampling budget allocation to image tiles based on their level of detail using DDIM. A common label is used to condition on augmentation and on real vs. simulated pairs, and is identity at inference. We describe the model, training and inference methods and present a pre-defined comparison and ablation methodology along with decision rules. No experiments have been performed and thus all potential advantages are presented as hypotheses. We also point out that the normalization used is equivalent to a transformation of the standard DDPM and thus any results are likely to be empirical rather than theoretical. Additionally, further research is needed into related work in order to verify novelty.

Index Terms – Image super-resolution, diffusion models, domain shift, frequency statistics, residual learning, adaptive sampling, data-efficient learning, remote sensing.

1. Introduction

   Existing super-resolution approaches tackle domain-specific and limited-data challenges through fragmented methods, including GANs prone to adversarial instability [2, 3, 5-7], augmentations that risk distribution bias [5], and frequency- specific analyses of domain shift [6, 7]. Meanwhile, current diffusion models rely on fixed sampling budgets and remain largely untested in low-data, domain-shifted scenarios [1, 8], while deployment costs and real-time constraints are frequently overlooked or unreported in prior literature [3, 5- 7, 9, 10].

   Research gap: The reviewed papers do not combine (i) a diffusion generator, (ii) a generative target normalized by measured domain statistics, and (iii) a sampling budget driven by the same statistics, in a setting diagnosed as

   frequency-shifted [6]. Whether such a combination improves stability, data efficiency, and average cost is an open empirical question.

   Motivation:DSN-RD (Domain-Statistics-Driven Residual Diffusion) estimates two quantities once, a residual spectrum and a detail-scale map, and uses them for the noise prior, a flatregion guard, and a per-tile compute allocator. A shared tag handles augmentation and simulated pairs.

   The contributions of this paper are:

   1. A formulation of conditional residual diffusion for SR in which the diffusion noise is shaped by an estimated domain spectrum and a predicted detail-scale map, trained with a plain noise-prediction loss and no discriminator.

   2. A tile-adaptive DDIM step budget driven by the same detail map, so that flat tiles receive fewer sampling steps than dense tiles.

   3. A shared tag that routes augmentation and simulated pairs through one conditioning mechanism, with spectrum estimation restricted to unaugmented data and identity tagging at inference.

   4. . A re-specified validation and ablation protocol with decision rules, including explicit criteria under which individual modules should be dropped.

   5. The components are potentially novel only in their combination; broader literature verification is required before any novelty claim (Section X)

2. RELATED WORK

   Papers [110] are the primary literature basis. Papers [4,6,9,10] were read at abstract level only, and their characterization here is correspondingly limited. Table I summarizes the.

   1. Diffusion-based vision and SR methods.

      Diffusion methods [1,8] provide the conditional DDPM/DDIM generative core used by DSN-RD. Their strengths are a simple regression-style loss and stable optimization. Their limitations for our set-ting are a single global sampling-step count and the absence of evaluation on domain-shifted and low-data tasks.

      Table 1: Comparison of Existing Methods (as characterized in the reviewed papers)

      Ref. Theme Limitation relevant to DSN-RD

      Table 2: DSN-RD Components and Corresponding Research Gaps

      Problem Component Status

      [1, 8] Diffusion Global step count; untested on domain- shifted, low-data SR
      [2, 3] Adversarial Training instability; deployment cost largely

      unreported [3]

      1. GAN, augmentation Augmentation can bias learned distribution;

         P1 Scarce data Unpaired spec-

         trum; simulated pairs (tag)

         P2 Domain shift Module 1 nor-

         malizer y

         Partial; hypothesis

         Addressed by design; unverified

      2. Frequency-aware SR

         instability

         Remedy remains adversarial; abstract-level

         P3 Augmentation shift

         Module 2 tag Unproven; no guarantee

         (CDGAN)

      3. Simulated pairs (un-

      reading

      Adversarial; other domain; syntheticreal

      P4 Instability No discriminator By removal; to be verified P5 Slow sampling Modules 1 and 3 Hypothesized

      derwater) gap P6 Deployment Module 3; effi- Partial

      1. One-class detection Discriminative; not an SR method cost ciency protocol

      2. DRL resource alloca- tion

      Networking problem; not an SR method P7 Flat-region hal- lucination

      Detail map m

      guard

      Hypoth

      4] Trust in GenAI Not algorithmic

      than a new diffusion theory.

   2. GAN-based and adversarial SR. Adversarial approaches [2, 3, 57] target realistic detail and are the reference approach for limited-data and domain-specific imaging. Their recurring limitation is training instability. DSN-RD responds by removal: it uses no discriminator and instead constrains hallucination through the detail-scale map and consistency projection.

   3. Domain- and frequency-aware methods. The frequency-aware analysis in [6] (CDGAN) diagnoses a fre- quency mismatch as a cause of SR failure in remote sensing, but the remedy remains adversarial. Paper [7] handles a dif- ferent domain (underwater color correction) and contributes the idea of simulated pairs. DSN-RD moves the frequency principle from the discriminator into the noise prior, and reuses simulated pairs through a tag; it does not claim to solve color correction.

   4. Data-efficient and augmentation-based approaches. Augmentation for data-limited GAN training raises the concern that augmentations leak into the learned distribution [5]. Simu- lated pairs [7] expand paired data at the risk of a synthetic-real gap. One-class detection without attacker data [9] addresses scarcity in a discriminaive form that DSN-RD does not target. DSN-RD uses a single tag for both, estimates the spectrum only on unaugmented data, and offers no guarantee against leak- age.

   5. Efficient sampling and deployment cost. Existing diffu- sion studies fix one step count for the whole image [1, 8]; GAN- based studies rarely report deployment cost [3, 57, 9]; and real- time constraints are stressed in a networking context [10]. Trust in generative outputs is a separate, non-algorithmic concern [4]. DSN-RD allocates steps per tile and specifies a standard effi- ciency protocol; it does not address communication-constrained resource allocation [10] or software-practice trust [4].

3. Problem Formulation and Research Gap

   1. Conditional SR

      Let x E RH×W denote an HR image and y = D(x) its LR obser- vation under a known or estimated degradation operator D(·) (noise omitted for brevity). Let U (·) be an upsampling oper- ator and y = U (y). The goal is to learn p(x | y) from a small

      paired set P = {(yi, xi) }, an unpaired HR set U , and option- ally a degradation simulator Deg(·), in a domain whose residual spectrum differs from that of natural images.

   2. Recurring problems

      Spot on. Those seven bottlenecks form the exact checklist of challenges that the DSN-RD frameworkwith its four-stage training pipeline, domain-statistics normalization, and adaptive samplingis engineered to solve. Let me know if you would like to dive deeper into any specific stage or component!

   3. Scope of DSN-RD

      Table II maps each problem to the DSN-RD mechanism and status. DSN-RD addresses P1P5 and P7 partially or hypothetically, and P6 only through an efficiency protocol and reduced average step count. It does not address non- Euclidean or discrete diffusion theory [1, 2, 8], spoof detection [9], communication-constrained resource allocation [10], or trust in generative AI [4]. It does not solve underwater color correction [7]; only the simulated-pair idea is reused, and transfer to other domains is a future test.

4. PROPOSED DSN-RD METHOD

   DSN-RD performs conditional SR in the residual domain with a diffusion model whose noise is shaped by domain statistics. The processing chain is: LR image upsampling detailscale prediction domain-statistics normalization tagged conditioning conditional diffusion U-Net tile-adaptive DDIM sampling residual refinement/projection HR image (Fig. 1). Upsampling and tiling. The LR image is upsampled to

   y, which serves as a low-band anchor, and split into overlapping tiles for memory-bounded, per-tile processing. Residual anchor. The network models only the residual R0 = x

   y, so low-band content is inherited from y rather than

   LR image y

   (tag = (a, w))

   Upsampling y= U(y)

   tiles

   Detail-scale predictor

   m = m (y)

   Module 1: normalizer

   Module 2: tagged

   conditioning

   m tile activity a j

   HR image

   x= y+R

   Projection

   R =yz0

   tile blending

   Module 3: tile-adaptive DDIM (Nb steps)

   Conditional U-Net

   Figure 1: Overall DSN-RD architecture (schematic; shaded blocks are the proposed modules). The same detail map m is used as noise prior, flat-region guard, and compute allocator. [Replace with final vector figure.]

   generated. This residual-plus-projection device is known out- Domain-statistics normalizer.

   side the reviewed corpus and is reused, not claimed.

   Detail-scale predictor. A network m predicts, from y alone, y =diag m (y) G , g() = max SR( )/S¯R /2, gmin ,

   a per-pixel residual scale map m. It is trained once (stage 1) and frozen. Because m is computed from the LR input, it is available at inference.

   Domain-statistics normalization (Module 1). The radi- ally averaged residual power spectral density (PSD) SR is es- timated once from unaugmented data and converted to a spec- tral gain G . Combined with m, it forms the normalizer

   y = diag(m) G , which scales and colors the diffusion noise to match the measured residual statistics. Diffusion then oper-

   ates in the normalized space, where the target has approximately unit scale.

   (2)

   where m (y) is the predicted per-pixel detail scale, clamped to [mmin, mmax]; SR() is the radially averaged residual PSD at ra- dial frequency , estimated once from unaugmented data (from

   R = x U (D(x)) for HR images; [confirm]); S¯R is the PSD ref- erence level ([confirm definition]); 0 controls the strength of spectral shaping; gmin > 0 is a gain floor; and G is the spec-

   tral gain operator with radial response g(). With the clamps,

   y is invertible.

   t 1

   Forward diffusion. With noise schedule {¯ t }T and ~

   =

   Tagged conditioning (Module 2). A tag = (a, w) records the applied augmentation a and a real/synthetic flag w for simu-

   N (0, I),

   Rt =

   ¯ t R0 +

   1 ¯ t y . (3)

   lated pairs. Augmentations and simulated pairs thus enter train- ing through one mechanism. The tag is dropped with probabil-

   Normalized diffusion space. With zt = y1Rt and z0 =

   y1R0,

   ity p during training and set to identity at inference, with the aim that the model can separate augmentation effects from the clean-

   zt =

   ¯ t z0 +

   1 ¯ t , (4)

   domain distribution. Spectrum-altering augmentations are ex- cluded from spectrum estimation. Whether the tag prevents leakage is unproven.

   Conditional diffusion U-Net. The denoiser receives the

   noisy normalized residual zt, timestep t, the conditioning [y, m],

   which is exactly the standard DDPM marginal. Module 1 is therefore a conditional preconditioning of the target, not a new diffusion process (see Section X).

   Noise-prediction loss.

   and , and predicts the noise with a plain 2 loss.

   Tile-adaptive DDIM sampling (Module 3). Each tiles

   2

   t

   L = E¨ (z ,t, [y, m], )¨ , (5)

   mean detail scale defines an activity aj; tiles are grouped into B

   buckets and sampled with bucket-specific DDIM step counts.

   Residual refinement and projection. The sampled normal- ized residual is mapped back by y, tiles are blended, and the component of R visible to D is removed before adding y.

   Three uses of the domain statistics. (i) Noise prior: y

   shapes the noise so that the prior matches the domains residual

   where [y,m] is channel-wise concatenation and = (a,w) is re- placed by a null tag with probability p.

   Detail-map loss (stage 1 only).

   q

   0

   Lmap = E¨log m (y) log(s + 0)¨ 2, s = B * R2, (6)

   where B is a local averaging kernel, * denotes convolution, R2

   statistics, addressing domain shift and data scarcity (P1, P2).

   (ii) Hallucination guard: where m is small, the reconstructed

   residual yz0 is small in amplitude, limiting spurious detail in

   0

   is the elementwise square, and 0 >

   s is the local residual scale.

   0 is a small constant. Thus

   flat regions (P7) without a discriminator (P4). (iii) Compute Tile activity. For tile j with pixel set ,j,

   allocator: the same m defines tile activity and step budgets (P5, a 1 m y u m (7)

   P6).

   j = | |

   ( )( ) ,

5. Mathematical Formulation

   uE j j

   Residual target.

   R0 = x y, y= U(y).

   where m is the median activity over the training set.

   Adaptive step budget. Thresholds {b }, set as quantiles of

   aj on the training set, define B buckets; tile j is in bucket b if

   Algorithm 1 DSN-RD Training Input: Paired set P, unpaired HR set U , operators U, D, optiona Deg, schedule{¯t}, T , , gmin, [mmin, mmax], augmentation family

   A , tag-dropout p, buckets B

   Output: , , G ,{b }

   1: Stage 0: estimate SR from unaugmented x E P uU ; build G

   (Eq. 2)

   2: Stage 1: train m with Lmap (Eq. 6); freeze

   Algorithm 2 DSN-RD Inference

   Input: LR image y; , , G , {b }; step counts {Nb }

   Output: x

   1: y= U(y); tile y with overlap; m = clamp(m (y)); y = diag(m)G

   2: compute aj per tile (Eq. 7); assign bucket b( j) (Eq. 8); group tiles by bucket

   3: for each bucket b do

   4: z ~ N (0, I) for its tiles; = identity

   3: Stage 2: for each iteration do

   5: for t in DDIM schedule with Nb steps do

   4: draw (y, x) ~ P, or (Deg(x), x) with x ~ U and w = synthetic 6: = (z,t, [y,m ],); z0 = (z 1 ¯t)/ ¯t

   5: draw a ~ A , apply jointly; = (a, w); with prob. p set = 0 7: z = ¯t 0 + ¯t (Eqs. 911)

   6: y= U(y); R0 = x y; m = clamp(m (y))

   7: y = diag(m)G ; z0 = 1R0

   z 1

   9: end for

   1

   y

   8: t ~ U {1..T }; ~ N (0, I); zt = ¯tz0 +

   9: update on (zt ,t, [y, m], ) 2 (Eq. 5)

   ¯t

   10: R = yz0 per tile; blend tiles; R R U(D(R )); x= y+R (Eq. 12)

   10: Stage 3: compute aj (Eq. 7) on training tiles; set {b} as quantiles

   1. Experimental Methodology

      This section outlines a proposed experimental plan with all

      b1 a j < b (with 0 = 0, B = ) and is sampled with Nb

      items marked [confirm] pending finalization, as no experiments

      DDIM steps,

      have yet been executed. The evaluation begins with Experiment

      N1 N2 ··· NB. (8) 0 as a motivation check, training plain conditional diffusion on

      the task from [6] to measure low-band consistency, flat-region

      The network is trained across all noise levels, so any DDIM spurious details, and radial PSD distance, where a lack of these

      grid is admissible. That few steps suffice for low-detail tiles is problems would shift the contribution toward data and

      a hypothesis.

      Reverse (DDIM) sampling. For consecutive timesteps t t

      on the buckets schedule,

      computational efficiency. The dataset selection includes two remote-sensing SR datasets from [6], a natural-image control such as DIV2K, and subsampled paired training sets at 100%, 25%, 10%, and 5% for low-data analysis, with scale factors,

      = (zt,t,[y,m],), (9) patch sizes, and splits still to be confirmed. Performance will be

      compared against multiple baselines, including CDGAN [6], an

      z0 = zt 1 ¯ t / ¯ t , (10) adapted DAG-style GAN [5], plain conditional diffusion on full

      images and residuals, and a standard regression SR network.

      zt = ¯ t z0 + 1 ¯ t . (11) Evaluation metrics encompass PSNR, SSIM, LPIPS, FID (used

      Residual reconstruction and projection.

      cautiously for small test sets), low-band consistency, radial PSD distance, flat-region spurious-detail energy, and run-to-run seed

      R =z0, R RU D(R) , x= y+R. (12) variance, alongside efficiency tracking for training time,

      y inference latency, peak memory, FLOPs, parameter counts, and

      The projection removes the part of R that D can observe; it en-

      bucket step counts across unspecified hardware. Finally, specialized experiments will evaluate domain-shift robustness

      forces low-band consistency when D(U (·)) id.

6. Training and Inference

   1. Training

      using matched versus mismatched sensor spectra, performance scaling across training fractions, augmentation impacts with and without conditioning tags, flat-region detail thresholds, and sampling efficiency comparing adaptive budgets against

      Training has four stages (Algorithm 1). Stage 0 estimates uniform allocations while verifying tile-boundary seam errors. SR from unaugmented data and builds G . Stage 1 trains

      and freezes m . Stage 2 trains on paired data and, optionally, simulated pairs from U , applying

      1. Expected Results and Discussion

         augmentations jointly to both images and recording them No measured results are available. The following are hypotheses

         in . Stage 3 calibrates bucket thresholds without to be tested, not findings. H1 Low-band consistency improves

         gradients.

   2. Inference

      At inference (Algorithm 2), the tag is set to identity, m is com- puted from y, tiles are bucketed by activity, and each bucket is sampled with its own DDIM schedule. Tiles are blended, pro- jected, and added to y.

      8: end for

      through the residual anchor and projection.

      Table 3: Experimental Evaluation Plan (no results yet)

      Experiment Comparison Measures

      Exp. 0 Plain diffusion vs. [6] task Low-band, flat-region,

      PSD

      Low-data 100/25/10/5% paired data PSNR, SSIM, LPIPS Domain shift Matched vs. mismatched PSD distance, fidelity

      spectrum

      Flat regions Full DSN-RD vs. no m guard Spurious-detail energy

      of U-Net evaluations per tile. With bucket fractions b, the av- erage step count is N¯ = b bNb, which is the quantity Module 3 aims to reduce relative to a uniform N; overlapping tiles add

      overhead and tile processing introduces blending cost. Module 3 targets the average, not the worst case. Numerical costs are to be measured.

      Limitations.

      Sampling Adaptive vs. uniform, equal mean steps

      Stability Seeds; no discriminator vs.

      GAN baselines

      Quality, latency, seams Run-to-run variance

      • Normalization equivalence: Eqs. (3) and (4) show that Mod- ule 1 is standard DDPM on a conditionally normalized tar- get. Any benefit is empirical, not theoretical.

      • Single point of failure: m serves as prior, guard, and alloca-

      H2 Flat-region hallucination is reduced because small m bounds residual amplitude there.

      H3 Domain-shift behavior improves when the noise prior matches the measured domain spectrum.

      H4 Data efficiency improves, with graceful degradation as the paired fraction shrinks, through the unpaired spectrum and tagged simulated pairs.

      H5 Average sampling cost falls, because flat tiles need fewer DDIM steps than dense tiles.

      H6 Training is stable without an adversarial discriminator, given the plain noise-prediction loss.

      Each hypothesis has a pre-set decision rule. If plain residual diffusion matches Module 1, the normalizer claim is dropped. If adaptive budgets do not beat uniform sampling at equal av- erage steps, Module 3 is dropped. If the tag does not reduce augmentation-induced shift, it is reported as unsupported. If Exp. 0 shows no low-frequency problem in plain diffusion, the motivation is reframed.

      1. Ablation Study

         Each configuration adds one element to the previous one: A0 Plain conditional DDPM: tests diffusion alone.

         A1 + Residual anchor: tests the known residual device.

         A2 + Module 1 (spectrum + detail map): tests domain-statistics normalization.

         A3 + Module 2 (tag, incl. simulated pairs): tests leakage han- dling.

         A4 + Module 3 (adaptive sampling): tests compute allocation at equal average steps.

         A5 Full DSN-RD: tests all components together.

         Additional studies: sensitivity (strength of spectral shaping); oracle detail map (an upper bound on the effect of m errors, using s instead of the prediction); no projection (contribution of consistency); tag on/off with a spectrum-altering augmenta- tion; number of tile buckets B; and paired vs. unpaired spectrum estimation. No ablation results are available.

      2. Complexity, Limitations, and Discussion

         Complexity (qualiative). Parameters: the U-Net plus the ad- ditional detail-map predictor m . Training: stage 0 is a one-time estimate, stage 1 adds a separate short training, stage 2 costs about that of a conditional diffusion model with an extra con- ditioning channel. Inference: the cost scales with the number

         tor, so errors in it degrade all three. Clamping, freezing, and the oracle ablation mitigate but do not remove this.

         • Degradation operator: anchoring and projection assume a known or well-estimated D; misregistered real data weakens both.

         • Tile seams: different step counts across neighbors can pro- duce boundary artifacts; overlap and blending are used and seam error must be measured.

         • Sensor/domain mismatch: a spectrum from a different sensor is a wrong prior.

         • Mispredicted detail: a dense tile judged flat receives too few steps; conservative thresholds and a floor N1 are proposed.

         • Remaining latency: diffusion still costs more than a single- pass GAN.

         • Unproven tag: no guarantee against augmentation leakage is claimed.

         • Overlap with existing work: residual and null-space- projected diffusion are known outside the reviewed corpus, and related ideas likely exist; the novelty, if any, lies in the choice and interaction of parts. Papers [4, 6, 9, 10] were read at abstract level only, and only ten papers were reviewed.

A broader literature search is required before any formal nov- elty claim, covering residual or colored-noise diffusion for SR, remote-sensing diffusion SR, augmentation-conditioned diffu- sion, null-space-projected diffusion SR, and spatially adaptive step allocation.

1. Conclusion

Diffusion-based SR in frequency-shifted domains faces scarce paired data, domain-shifted statistics, augmentation- induced bias, adversarial instability, and sampling cost, and the reviewed literature does not combine a diffusion generator with domainstatistics normalization and statistic-driven compute allocation. DSN-RD estimates a residual spectrum and a detail-scale map once and uses them as the noise prior, a flat-region guard, and a tile-level step allocator, together with a shared tag for augmentation and simulated pairs. Expected benefits are hypotheses only: better low-band consistency, less flat-region hallucination, better data efficiency, lower average sampling cost, and stable training without a discriminator. Their validation through the pre-specified experiments and ablations is the next step, and no superiority is claimed before it.

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