IS-Diff: Seed-Based Diffusion Refinement

• IS-Diff is a diffusion paradigm that begins with a task-aligned seed and refines residual errors instead of generating from pure noise.
• It leverages diverse seed construction strategies—such as learned priors, input-derived cues, and retrieval-based methods—to enhance context preservation.
• Empirical results across applications like inpainting, segmentation, speaker recognition, robotics, and CT reconstruction demonstrate improved quality and robustness.

Initial Seed Refined Diffusion Model (IS-Diff) denotes a seed-to-refinement diffusion paradigm in which generation or reconstruction begins from an initial state already aligned with task structure, and diffusion is used primarily to refine residual error rather than to synthesize the entire sample from an unconstrained standard Gaussian start. The name appears explicitly in the inpainting method "IS-Diff: Improving Diffusion-Based Inpainting with Better Initial Seed" (Lyu et al., 15 Sep 2025), but the same design pattern is used to interpret several other systems: Residual Prior Diffusion (RPD) for generative modeling (Kutsuna, 25 Dec 2025), G4Seg for inexact segmentation refinement (Zhang et al., 2 Jun 2025), SEED for speaker embedding enhancement (Nam et al., 22 May 2025), R2-Diff for robot motion prediction (Oba et al., 2023), and Diff-NAF for stationary CT reconstruction (Fang et al., 18 Nov 2025). A complementary line of work shows why this emphasis on initialization matters: latent diffusion can be highly brittle to small perturbations of the initial seed vector (Po-Yuan et al., 2023).

1. Definition and conceptual scope

In vanilla diffusion, the reverse process is typically initialized from pure noise, often $x_T \sim \mathcal{N}(0, I)$ or its latent-space analogue. IS-Diff replaces or augments that default with a seed that already carries global semantics, coarse geometry, retrieval context, observed-mask information, or physics-consistent structure. The refinement model then denoises or corrects the seed toward the target distribution rather than learning the entire mapping from scratch.

This definition covers both explicit and implicit uses of the term. In inpainting, IS-Diff is a named, training-free procedure that samples “distributional harmonious seeds” from unmasked regions and dynamically strengthens the seed prior when intermediate generations become unharmonious (Lyu et al., 15 Sep 2025). In RPD, the same pattern appears as a coarse prior model followed by diffusion over the residual between the prior and the target data distribution (Kutsuna, 25 Dec 2025). In G4Seg, a coarse segmentation mask is the initial seed, and diffusion-based generation is used to refine it via discrepancy analysis (Zhang et al., 2 Jun 2025). In SEED, the seed is a speaker embedding from a fixed recognizer, refined by a diffusion denoiser into a clean-like embedding (Nam et al., 22 May 2025). In R2-Diff, the seed is a retrieved motion trajectory, refined through reverse diffusion conditioned on the test image (Oba et al., 2023). In Diff-NAF, an initially trained Neural Attenuation Field functions as the seed model whose synthesized projections are then diffusion-refined and recycled as pseudo-labels (Fang et al., 18 Nov 2025).

A common misconception is that IS-Diff names a single architecture. The literature instead supports a broader characterization: it is a modeling principle in which initialization is task-aware, and diffusion is delegated to refinement, correction, or residual completion. Another misconception is that IS-Diff must be training-free. The inpainting variant is explicitly training-free (Lyu et al., 15 Sep 2025), but RPD, SEED, R2-Diff, and Diff-NAF all involve learned refinement models (Kutsuna, 25 Dec 2025).

2. Canonical mechanics

The mathematical backbone remains the standard diffusion formalism. A representative forward process is

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

with cumulative product $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$ and closed form

$$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$

What changes in IS-Diff is the role of the start state. Instead of treating the reverse chain as beginning from an unconditional random sample, many IS-Diff systems define a seed $x_{\mathrm{seed}}$ or a coarse latent state and then either start directly from that seed or inject controlled noise at an intermediate timestep,

$$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$

This pattern is explicit in R2-Diff, where a retrieved motion $m_0(k)$ is noised to step $n^\star$ and then denoised from $n^\star$ to $0$ (Oba et al., 2023). SEED uses the same logic in embedding space, treating the backbone embedding as a diffused state at a fixed timestep $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$0 and directly denoising it to a refined embedding (Nam et al., 22 May 2025). In inpainting, the primary seed is first composed from observed and sampled masked content and then forward-noised to a start timestep $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$1; if disharmony is detected, $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$2 is reduced so that the seed exerts stronger influence (Lyu et al., 15 Sep 2025).

RPD provides the most explicit probabilistic formulation of this idea. Its prior factorization is

$$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$3

and the reverse chain starts from $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$4 rather than from standard Gaussian noise. The residual parameterization

$$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$5

induces prior-centered coordinates in which the forward diffusion becomes standard, while the reverse denoiser is conditioned on $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$6, $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$7, $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$8, and auxiliary variables (Kutsuna, 25 Dec 2025). This makes the seed not merely a heuristic initialization, but part of an explicit generative model with a tractable ELBO.

3. Seed construction strategies

IS-Diff systems differ mainly in how the seed is produced and what residual the diffusion model is expected to remove.

Instantiation	Initial seed	Refinement target
RPD	$$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$9 from a coarse prior	Residual between prior and target distribution
Inpainting IS-Diff	GMM-sampled masked seed from unmasked content	Harmonious completion in masked region
G4Seg	Coarse foreground mask $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$0	Foreground probability and boundary refinement
SEED	Backbone speaker embedding $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$1	Clean-like robust embedding
R2-Diff	Retrieved motion trajectory	Contextually appropriate motion
Diff-NAF	Initial NAF and synthesized projections	Refined pseudo-label projections for CT

A first family uses learned coarse priors. RPD allows $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$2 to come from a VAE, $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$3-VAE, VQ-VAE, or structured mixture-of-Gaussians, and uses the decoder outputs $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$4 and $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$5 both to initialize the reverse chain and to condition the denoiser (Kutsuna, 25 Dec 2025). This separates global manifold structure from fine-scale local detail.

A second family uses input-derived seeds. In inpainting, IS-Diff fits a $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$6 Gaussian Mixture Model on unmasked pixels or latent codes, samples masked content from that estimated distribution, composes a primary seed, and adds a small perturbation for diversity (Lyu et al., 15 Sep 2025). The point is not semantic hallucination from scratch, but initialization from a distribution judged statistically compatible with the visible image context.

A third family uses coarse task-specific seeds. G4Seg takes an inexact segmentation mask $\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$7 as the seed and exploits discrepancies between the original image and a mask-conditional Stable Diffusion reconstruction to update per-pixel foreground probabilities via

$\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$8

The refinement step is thus diffusion-mediated but expressed in segmentation space (Zhang et al., 2 Jun 2025).

A fourth family uses retrieval or observation-based seeds. R2-Diff retrieves a motion from the training set using image features along the motion trajectory and refines that motion rather than sampling from random noise (Oba et al., 2023). SEED takes speaker embeddings from a fixed recognizer as seeds and reconstructs them toward the clean embedding target without speaker labels (Nam et al., 22 May 2025). Diff-NAF begins from a physics-grounded but incomplete NAF reconstruction, synthesizes missing-angle projections, and diffusion-refines those synthesized projections before reusing them as pseudo-labels (Fang et al., 18 Nov 2025).

These variants suggest that “initial seed” is not tied to one datatype. It can be a sample, latent tensor, probability map, trajectory, embedding, projection image, or even an entire coarse model.

4. Conditioning, residualization, and refinement control

A central technical feature of IS-Diff is that refinement is usually easier when performed in coordinates centered on the seed or prior. RPD makes this explicit through

$\bar{\alpha}_t = \prod_{s=1}^t \alpha_s$9

so that the forward process on $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$0 mirrors standard diffusion. It also introduces auxiliary variables

$$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$1

which are analytically close to the regression targets in noise- and velocity-prediction. The associated propositions show that as $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$2 and/or $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$3 adapts, the expected squared error between these auxiliaries and the true targets shrinks, reducing denoising difficulty (Kutsuna, 25 Dec 2025).

In the inpainting method explicitly called IS-Diff, control is implemented through Dynamic Selective Refinement (DSR) rather than through auxiliary variables. At checkpoint timestep $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$4, a histogram-based distributional cross-entropy

$$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$5

is computed between masked and unmasked regions. If $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$6 with default $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$7, the start timestep is reduced by $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$8, increasing the effective prior weight $$x_t = \sqrt{\bar{\alpha}_t}\, x_0 + \sqrt{1-\bar{\alpha}_t}\, \epsilon, \qquad \epsilon \sim \mathcal{N}(0,I).$$9 and restarting sampling from a less noisy seed (Lyu et al., 15 Sep 2025). Refinement strength is therefore adjusted adaptively in response to observed disharmony.

G4Seg uses a different conditioning mechanism: explicit mask injection into Stable Diffusion self-attention and cross-attention via

$x_{\mathrm{seed}}$0

followed by semantic correspondence alignment with a frozen CLIP image encoder. The diffusion model is not retrained; it is used as a structured generator whose reconstruction discrepancy becomes a refinement signal for segmentation (Zhang et al., 2 Jun 2025).

Diff-NAF exemplifies iterative refinement control in inverse problems. Its Angle-Prior Guided Projection Synthesis chooses new projection angles, and its Diffusion-driven Reuse Projection Refinement Module applies a dual-branch residual-and-noise diffusion model to synthesized projections. The refined projections are then inserted back into the training set with pseudo-label weight $x_{\mathrm{seed}}$1, coupling refinement to later physics-consistent optimization (Fang et al., 18 Nov 2025).

5. Empirical behavior across application domains

In image generation, RPD reports that standard diffusion models fail to capture fine details on hetero-scale synthetic datasets, whereas RPD preserves global structure from the prior and adds fine details via residual diffusion. On Butterflies $x_{\mathrm{seed}}$2, few-step quality is strong: at 3 inference steps, KID@3 is $x_{\mathrm{seed}}$3 for RPD and $x_{\mathrm{seed}}$4 for RPD_vpred, compared with $x_{\mathrm{seed}}$5 for DDPM, $x_{\mathrm{seed}}$6 for DDIM, $x_{\mathrm{seed}}$7 for v-pred, $x_{\mathrm{seed}}$8 for DiffuseVAE, $x_{\mathrm{seed}}$9 for Rectified Flow, and $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$0 for IMM. Its 1WD@3 of $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$1 is reported as best among all methods, and strong few-step behavior is retained with as few as 3–10 steps (Kutsuna, 25 Dec 2025).

In free-form inpainting, explicit IS-Diff improves several pretrained samplers without additional training. On ImageNet 1K with Wide/Half/Expand masks, Stable Inpainting improves from LPIPS $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$2 and FID $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$3 to LPIPS $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$4 and FID $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$5 when combined with IS-Diff. RePaint improves from LPIPS $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$6 and FID $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$7 to LPIPS $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$8 and FID $$x_{t^\star} = \sqrt{\bar{\alpha}_{t^\star}}\, x_{\mathrm{seed}} + \sqrt{1-\bar{\alpha}_{t^\star}}\, \epsilon.$$9. On CelebA-HQ 1K, DDNM plus IS-Diff reduces Expand-mask FID from $m_0(k)$0 to $m_0(k)$1 while preserving Wide-mask LPIPS at $m_0(k)$2 (Lyu et al., 15 Sep 2025).

In segmentation refinement, G4Seg is training-free and reports consistent mIoU gains across PASCAL VOC12, PASCAL Context, and MS COCO Object 2014. For training-free text-supervised segmentation, +SCLIP improves VOC12 from $m_0(k)$3 to $m_0(k)$4, Context from $m_0(k)$5 to $m_0(k)$6, and COCO from $m_0(k)$7 to $m_0(k)$8; +DiffSegmenter improves VOC12 from $m_0(k)$9 to $n^\star$0. In weakly supervised segmentation, +CLIP-ES raises Seed mIoU from $n^\star$1 to $n^\star$2 and Mask mIoU from $n^\star$3 to $n^\star$4. Module ablations on VOC12 show Baseline Seed $n^\star$5, +Explicit Mask Injection $n^\star$6, +Semantic Correspondence Alignment $n^\star$7, and +CF-[0.2,0.6] $n^\star$8 (Zhang et al., 2 Jun 2025).

In speaker recognition, SEED operates as a post-hoc embedding refiner and reports up to $n^\star$9 improvement on environmental mismatch sets while retaining conventional performance. With an ECAPA-TDNN backbone, VoxSRC23 EER improves from $n^\star$0 to $n^\star$1 and minDCF from $n^\star$2 to $n^\star$3; VC-Mix EER improves from $n^\star$4 to $n^\star$5. Generalization sets remain stable, with Vox1-O EER moving from $n^\star$6 to $n^\star$7 and Vox1-H from $n^\star$8 to $n^\star$9. Single-step refinement at $0$0 shows negligible difference from multi-step DDIM sampling in this embedding setting (Nam et al., 22 May 2025).

In robot manipulation, R2-Diff reports average success rate $0$1 across 16 RLBench tasks, compared with $0$2 for DMO-EBM, $0$3 for Diffusion Policy, $0$4 for RT1, and $0$5 for VINN. Task-level examples include Place cups at $0$6 versus $0$7 for DMO-EBM and $0$8 for Diffusion Policy, Reach target at $0$9 versus $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$00 and $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$01, and Push buttons at $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$02 versus $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$03 and $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$04. Ablations show that retrieval helps only when the diffusion schedule is tuned for seed refinement: with a traditional schedule, retrieval yields average $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$05 versus $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$06 for random initialization, whereas with the R2-Diff schedule it yields $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$07 versus $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$08 (Oba et al., 2023).

In stationary CT reconstruction, Diff-NAF reports best PSNR/SSIM under ultra-sparse-view conditions. For 50-view reconstruction, Head improves from NAF $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$09 dB / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$10 to Diff-NAF $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$11 dB / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$12; Jaw improves from $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$13 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$14 to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$15 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$16; Box improves from $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$17 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$18 to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$19 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$20. For 20-view reconstruction, Head improves from $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$21 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$22 to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$23 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$24, and Box from $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$25 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$26 to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$27 / $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$28 (Fang et al., 18 Nov 2025).

6. Reliability, limitations, and design implications

The strongest argument for IS-Diff as a general paradigm is that initial conditions measurably matter. In latent-based Stable Diffusion v2.1, the no-shift baseline yields Top-1 $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$29, Top-5 $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$30, and CLIPScore $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$31. Slight positive shifts can help marginally, but larger seed perturbations rapidly collapse conditioning. For Random Shift at $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$32, Top-1 falls to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$33 and Top-5 to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$34; for Mean Shift at $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$35, Top-1 falls to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$36 and Top-5 to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$37; for Standard Deviation Shift at $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$38, both Top-1 and Top-5 drop to $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$39; for Arrangement Shift, $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$40 yields Top-1 $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$41, and $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$42 yields Top-1 and Top-5 of $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$43. GLIDE is reported to remain comparatively unaffected by such seed shifts, and classifier-free guidance improves robustness relative to no guidance (Po-Yuan et al., 2023).

These findings do not imply that a stronger seed is always preferable. RPD notes that if the prior capacity is too small, very few-step sampling can inherit its limitations, including reduced color diversity; this can be mitigated by using more steps or a better prior (Kutsuna, 25 Dec 2025). G4Seg reports limited gains when initial seeds are very poor, especially at IoU below $$q(x_t \mid x_{t-1}) = \mathcal{N}\bigl(x_t; \sqrt{\alpha_t}\, x_{t-1}, (1-\alpha_t) I\bigr),$$44, and notes sensitivity under ambiguous boundaries, severe occlusions, and domains where Stable Diffusion priors are weak (Zhang et al., 2 Jun 2025). SEED identifies instability when the clean–noisy embedding gap becomes large, since training assumes paired clean and noisy embeddings remain relatively close (Nam et al., 22 May 2025). R2-Diff depends on retrieval quality and on schedule tuning matched to nearest-neighbor distance statistics; refinement can even reduce success when the retrieved motion is already nearly perfect or substantially out of distribution relative to the Gaussian noising assumption (Oba et al., 2023). Diff-NAF can propagate subtle bias through pseudo-label reuse, and inter-view inconsistencies may arise if the diffusion prior disturbs angular coherence (Fang et al., 18 Nov 2025).

A plausible synthesis is that IS-Diff is most effective when the seed supplies reliable coarse structure and diffusion is reserved for residual correction. Across the literature, several design rules recur: start the reverse chain from a task-aligned prior rather than an unconditional Gaussian; condition the denoiser on seed statistics or context; use auxiliary variables, discrepancy measures, or restart logic to reduce refinement difficulty; and evaluate not only final sample quality but also sensitivity to initialization, especially in latent-space systems. In that sense, IS-Diff is less a narrow model family than a general strategy for redistributing work between initialization and denoising, with the seed carrying global or structural burden and diffusion concentrating on refinement.