Retrieval-Augmented Initialization with Dual-Guided Inversion for Flow-Based Inverse Problem Solvers

Hansam Cho; Seoung Bum Kim

cs.CVOct 30, 2026

Retrieval-Augmented Initialization with Dual-Guided Inversion for Flow-Based Inverse Problem Solvers

Authors: Hansam Cho, Seoung Bum Kim

Organizations: Department of Industrial and Management Engineering, Korea University

Abstract

Flow models have recently emerged as powerful generative priors for solving inverse problems. Despite their success, most existing flow-based inverse problem solvers initialize the reconstruction process with random Gaussian noise. However, recent studies in image generation have shown that the choice of initial noise can significantly influence generation outcomes. The role of initialization as a distinct design choice in flow-based inverse problem solving remains comparatively underexplored. In this work, we systematically evaluate noise initialization strategies while holding the downstream flow-based inverse solver fixed. We propose Retrieval-Augmented Initialization with Dual-Guided Inversion (RA-DGI), a method that constructs improved initial noise by leveraging retrieved proxy clean images and dual-guided inversion. Extensive experiments across multiple inverse problems demonstrate that the quality of the initial noise substantially affects reconstruction fidelity and perceptual performance. RA-DGI outperforms standard random initialization and achieves superior results compared to inference-time scaling strategies, while requiring less computational overhead. These findings highlight initialization as a critical yet previously overlooked factor in flow-based inverse problem solvers.

Figures & tables

Figure 2: Overview of RA-DGI. (a) Retrieval-augmented initialization. A proxy clean image $x_{0}^{\ast}$ is retrieved from a dataset using semantic features extracted by $\phi(\cdot)$ and used as the starting point for inversion. (b) Dual-guided inversion. Measurement guidance (blue) enforces measurement consistency, while prior guidance (red) applies Gaussian regularization to encourage compatibility with the source prior, jointly refining the latent trajectory.

AFHQ
Method	Super-Resolution				Deblurring				Denoising				Compressed Sensing
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
Random	23.34 (0.050)	0.477 (0.004)	0.235 (0.004)	21.91 (0.763)	22.79 (0.021)	0.464 (0.003)	0.254 (0.004)	24.76 (1.272)	21.92 (0.015)	0.446 (0.004)	0.301 (0.004)	31.22 (0.720)	20.25 (0.006)	0.423 (0.003)	0.353 (0.004)	41.72 (1.104)
NPNet	23.18 (0.067)	0.474 (0.003)	0.240 (0.007)	24.41 (1.159)	22.59 (0.061)	0.453 (0.003)	0.261 (0.006)	26.62 (1.306)	21.93 (0.060)	0.446 (0.003)	0.293 (0.005)	33.24 (1.330)	20.35 (0.061)	0.416 (0.003)	0.338 (0.003)	42.17 (1.227)
RF-Inversion	23.94 (0.064)	0.529 (0.004)	0.287 (0.000)	22.95 (1.104)	23.22 (0.057)	0.486 (0.003)	0.299 (0.004)	23.83 (0.693)	22.05 (0.075)	0.406 (0.005)	0.243 (0.003)	28.27 (0.473)	22.32 (0.053)	0.441 (0.002)	0.267 (0.007)	29.97 (0.868)
RA-DGI (Ours)	24.03 (0.101)	0.537 (0.003)	0.236 (0.007)	21.92 (0.768)	23.57 (0.115)	0.528 (0.003)	0.266 (0.006)	24.69 (0.668)	22.85 (0.085)	0.475 (0.002)	0.266 (0.004)	28.38 (0.286)	22.69 (0.025)	0.454 (0.000)	0.262 (0.001)	29.72 (0.229)

Table 1: Quantitative comparison on four inverse problems across three datasets. Values are reported as the mean over three seeds, with the sample standard deviation shown in parentheses. Best and second-best mean values are shown in bold and underline , respectively.

Figure 3: Qualitative comparison on four inverse problems. The displayed examples illustrate improved structural fidelity and detail with RA-DGI

Figure 4: Effect of inference-time scaling compared with our initialization strategy. The x-axis shows inference-time compute (NFE), and the y-axis shows reconstruction metrics (PSNR, SSIM, LPIPS). Although some search configurations achieve higher SSIM, RA-DGI offers a more favorable tradeoff between reconstruction quality and NFE, achieving better PSNR and LPIPS with substantially fewer function evaluations.

Method	Component			Super-Resolution				Deblurring
Method	Retrieval	Prior	Meas.	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
w/o retrieval	$\times$	$\checkmark$	$\checkmark$	23.37	0.492	0.313	31.11	22.62	0.439	0.299	31.06
w/o prior guidance	$\checkmark$	$\times$	$\checkmark$	24.52	0.580	0.275	21.98	24.13	0.580	0.314	25.95
w/o measurement guidance	$\checkmark$	$\checkmark$	$\times$	23.59	0.473	0.231	23.63	23.22	0.470	0.261	26.03
RA-DGI (Ours)	$\checkmark$	$\checkmark$	$\checkmark$	24.02	0.534	0.236	21.03	23.57	0.525	0.267	23.94

Table 2: Ablation study of the proposed components. We analyze the contributions of retrieval-augmented initialization, prior guidance, and measurement guidance. Best and second-best results are highlighted in bold and underline , respectively.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Size	Encoder	Dataset	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
100	DINOv3	Unsplash	24.27(0.17)	0.564(0.018)	0.206(0.005)
1000			24.24(0.09)	0.562(0.006)	0.202(0.006)
10000			24.39(0.06)	0.572(0.002)	0.198(0.001)
1000	DINOv3	Unsplash	24.28	0.571	0.195
	VAE		23.84	0.505	0.205
	None		23.71	0.486	0.231

Appendix

Table 3: Retrieval analysis results

	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Shuffled	23.73	0.509	0.202
Nearest neighbor	24.28	0.571	0.195

Appendix

Table 4: Ablation of the retrieval strategy.

Inversion method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Ordinary inversion	24.38	0.559	0.233
Dual-guided inversion	24.28	0.571	0.195

Appendix

Table 5: Ablation of the inversion method.

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
Random (Solve 30)	24.55	0.618	0.182
RA-DGI (Inv. 10 + Solve 20)	24.56	0.621	0.178

Appendix

Table 6: Compute-matched comparison.

Dataset	Task	Random	NPNet	RF-Inversion	RA-DGI
AFHQ	SR	$0.0055$	$0.0058$	$\underline{0.0049}$	$\mathbf{0.0039}$
	Deblur	$0.0056$	$0.0059$	$\underline{0.0055}$	$\mathbf{0.0036}$
	Denoise	$0.0273$	$0.0270$	$\underline{0.0266}$	$\mathbf{0.0220}$
	CS	$0.0317$	$0.0411$	$\underline{0.0177}$	$\mathbf{0.0154}$
FFHQ	SR	$0.0080$	$0.0105$	$\underline{0.0067}$	$\mathbf{0.0044}$
	Deblur	$0.0081$	$0.0097$	$\underline{0.0074}$	$\mathbf{0.0043}$

Appendix

Table 7: Measurment consistency results.

Method	Time/image (s) $\downarrow$
Random	5.9
NPNet	6.1
RF-Inversion	6.3
RA-DGI	11.2

Appendix

Table 8: Per-image wall-clock latency.

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
FLAIR	23.99	0.596	0.538
FLAIR + RA-DGI	24.03	0.600	0.532

Appendix

Table 9: Compatibility with FLAIR.

Figure 6: Failure cases on tasks where the underlying solver is weak. Even with the proposed initialization, it remains difficult to overcome the inherent limitations of the original solver.

Figure 7: Additional qualitative comparisons on the AFHQ dataset.

Figure 8: Additional qualitative comparisons on the FFHQ dataset.

Figure 9: Additional qualitative comparisons on the DIV2K dataset.

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Flow-based generative models have emerged as powerful priors for solving inverse problems. One option is to directly optimize the initial latent code (noise), such that the flow output solves the inverse problem. However, this requires backpropagating through the entire generative trajectory, incurring high memory costs and numerical instability. We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code. By enforcing the flow dynamics locally and coupling segments through trajectory-matching penalties, MS-Flow alternates between updating intermediate latent states and enforcing consistency with observed data. This reduces memory consumption while improving reconstruction quality. We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.

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