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When Latents Forget Pixels: Restoring Fidelity in Diffusion Transformer Super-Resolution
Yu Shi, Yuyao Zhang, Yu-wing Tai
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Abstract
Abstract:Image super-resolution (SR) with large generative models has recently achieved remarkable perceptual quality, yet maintaining fidelity to the LR observation remains challenging. In particular, we observe that diffusion transformers (DiTs) built on latent representations suffer from a critical limitation: the compression bottleneck of the VAE weakens fine-grained spatial information, leading to hallucinated details that are weakly grounded in the input image. In this work, we revisit generative SR from a representation perspective and propose a pixel-grounded super-resolution (PGSR) framework that preserves LR-observed pixel evidence before VAE compression and reuses it throughout restoration. Instead of relying solely on the compressed latent condition, PGSR extracts pre-VAE pixel evidence from the upsampled LR image and reuses it at two stages. First, Condition-Side Trajectory Guidance fuses LR-derived pixel evidence with the latent LR condition to guide the latent restoration trajectory. Second, Decoder-Side Pixel Grounding injects multi-scale pixel features into the frozen VAE decoder to ground the final rendering with LR-observed cues. To efficiently adapt large pretrained DiT models, we keep the latent autoencoder and main flow-matching backbone frozen, and train only lightweight restoration modules. We further study an efficient local-window attention variant for improved high-resolution efficiency and scalability. Extensive experiments demonstrate that PGSR improves the realism--fidelity trade-off and produces more faithful, visually convincing results than existing latent generative SR approaches.
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- Source: https://arxiv.org/abs/2608.09133v1
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When Latents Forget Pixels: Restoring Fidelity in Diffusion Transformer Super-Resolution Yu Shi Dartmouth College Yuyao Zhang Dartmouth College Yu-Wing Tai Dartmouth College Abstract Image super-resolution (SR) with large generative models has recently achieved remarkable perceptual quality, yet maintaining fidelity to the LR observation remains challenging. In particular, we observe that diffusion transformers (DiTs) built on latent representations suffer from a critical limitation: the compression bottleneck of the VAE weakens fine-grained spatial information, leading to hallucinated details that are weakly grounded in the input image. In this work, we revisit generative SR from a representation perspective and propose a pixel-grounded super-resolution (PGSR) framework that preserves LR-observed pixel evidence before VAE compression and reuses it throughout restoration. Instead of relying solely on the compressed latent condition, PGSR extracts pre-VAE pixel evidence from the upsampled LR image and reuses it at two stages. First, Condition-Side Trajectory Guidance fuses LR-derived pixel evidence with the latent LR condition to guide the latent restoration trajectory. Second, Decoder-Side Pixel Grounding injects multi-scale pixel features into the frozen VAE decoder to ground the final rendering with LR-observed cues. To efficiently adapt large pretrained DiT models, we keep the latent autoencoder and main flow-matching backbone frozen, and train only lightweight restoration modules. We further study an efficient local-window attention variant for improved high-resolution efficiency and scalability. Extensive experiments demonstrate that PGSR improves the realism–fidelity trade-off and produces more faithful, visually convincing results than existing latent generative SR approaches. Figure 1: Super-resolution results using PGSR compared to one of the other State-of-the-art pixel-guided methods. While it produces visually plausible textures, it hallucinates structures inconsistent with the input (e.g., incorrect texts or unexpectedly sharpened edges). Our method preserves LR pixel features before VAE compression and uses them to guide latent trajectory and ground final rendering, producing sharper results that remain faithful to the LR observation. 1 Introduction Image super-resolution (SR) recovers high-frequency details from a low-resolution (LR) input while it requires preserving strict fidelity to the observed image. Recent approaches leverage large pretrained generative models, including diffusion and transformer-based architectures, to synthesize realistic textures that exceed the capabilities of regression- or GAN-based methods (Ledig et al., 2017; Wang et al., 2018; Saharia et al., 2021; Wang et al., 2023b; Wu et al., 2023). However, despite their strong perceptual quality, these methods still struggle to remain consistent with the input, often hallucinating details that are only weakly supported by the LR image. In this work, we identify a key but underexplored reason for this failure: latent generative models operate on compressed representations that can weaken fidelity-critical pixel evidence. Modern diffusion transformers and latent diffusion models rely on a VAE tokenizer Kingma and Welling (2014); Rombach et al. (2022) to map images into a compact latent space. While this enables efficient high-resolution generation, it also introduces an information bottleneck that removes subtle spatial cues and high-frequency structures essential for faithful SR. As illustrated in Fig. 1, even when conditioned on the LR input, latent-only generation tends to produce visually convincing but incorrect details, revealing a fundamental mismatch between latent generative priors and pixel-level restoration objectives. This perspective suggests that improving SR is not merely a matter of stronger conditioning, but of keeping LR-observed image evidence accessible before it is compressed into the latent space. Prior works have attempted to mitigate this issue by introducing pixel-aware guidance or additional control mechanisms within diffusion-based SR pipelines (Wu et al., 2023; Yang et al., 2024; Sun et al., 2025; Arora et al., 2025). While effective, most of these designs still use pixel evidence primarily as an external condition for the latent denoiser. They therefore leave two fidelity gaps only partially addressed: the latent guided trajectory may drift away from LR-observed structure, and the frozen decoder may further lose spatial detail during final rendering. To this end, we propose a pixel-grounded super-resolution (PGSR) framework that explicitly preserves LR-observed pixel cues before VAE compression and reuses them throughout restoration. We refer to this design as Pixel-Grounded Guidance: pixel evidence denotes image-domain features extracted from the LR input before VAE compression and used to restore fidelity-critical spatial information. PGSR realizes this idea through two complementary mechanisms. First, Condition-Side Trajectory Guidance fuses LR-derived pixel evidence into the ControlNet condition to anchor the flow trajectory. Second, Decoder-Side Pixel Grounding injects multi-scale pixel features into the frozen VAE decoder to recover fine spatial structures at rendering time. In this way, the pretrained latent backbone provides strong semantic and generative priors, while the pixel-grounded pathway constrains restoration with LR-observed image evidence. Importantly, our design differs from existing pixel-guided SR methods in that pixel evidence is not only appended as an auxiliary condition. Instead, it is used to ground both what content is generated in latent space and how that content is decoded back into pixels. By explicitly modeling the residual information missing from the latent space, our approach directly targets the root cause of fidelity degradation in generative SR. To enable practical deployment on large pretrained models, we adopt a parameter-efficient adaptation strategy based on a ControlNet-style architecture (Zhang et al., 2023), where the diffusion transformer backbone remains frozen and only lightweight modules are trained. We further adapt the frozen flow-matching transformer with low-rank adapters and local-window attention to improve high-resolution efficiency. In summary, our contributions are three-fold: • We identify latent compression as a fundamental bottleneck in generative super-resolution, and reinterpret SR as a mismatch between latent generative priors and pixel-faithful restoration. • We propose Pixel-Grounded Guidance, a dual-stage design that reuses pre-VAE pixel evidence to guide both latent trajectory formation and final image decoding, improving fidelity throughout the restoration process. • We present a practical and efficient implementation on pretrained latent flow-matching models, using lightweight adaptation and local attention to achieve a better realism–fidelity trade-off. 2 Related Works Generative Super-Resolution and the Realism–Fidelity Trade-off. Early super-resolution (SR) methods focused on distortion minimization, optimizing metrics such as PSNR and SSIM (Wang et al., 2004), with representative models including SRCNN (Dong et al., 2014), VDSR (Kim et al., 2016), and transformer-based restorers such as SwinIR (Liang et al., 2021). While effective on distortion metrics, these approaches often produce over-smoothed results. Perceptual SR methods emphasize visual realism instead. SRGAN (Ledig et al., 2017) and ESRGAN (Wang et al., 2018) show that adversarial training and perceptual losses (Johnson et al., 2016; Zhang et al., 2018b) yield sharper, more realistic textures. This shift is formalized by the perception–distortion trade-off (Blau and Michaeli, 2018), where improved perceptual quality often reduces fidelity. GLEAN (Chan et al., 2021) further leverages pretrained generative priors for large-scale SR. For real-world SR, degradation modeling is critical. BSRGAN and Real-ESRGAN (Zhang et al., 2021; Wang et al., 2021) highlight the importance of realistic blur–noise–compression pipelines. Diffusion-based SR improves perceptual quality and stability: SR3 (Saharia et al., 2021) and DDRM (Kawar et al., 2022) introduce diffusion priors, while ResShift (Yue et al., 2023), SinSR (Wang et al., 2023c), and OSEDiff (Wu et al., 2024) improve efficiency. Recent work explores rectified-flow formulations such as FlowSR and FluxSR (Xu et al., 2025; Li et al., 2025). Another direction adapts pretrained generative priors, such as StableSR (Wang et al., 2023b), DiffBIR (Lin et al., 2024), XPSR (Qu et al., 2024), and SeeSR (Wu et al., 2023), to enhance restoration via semantic and structural conditioning. Despite these advances, the realism–fidelity trade-off persists: stronger generative priors improve perceptual quality by relaxing constraints from the LR input, often introducing hallucinated details. Limitations of Latent-Space Diffusion for Restoration. Latent diffusion models (LDMs) (Rombach et al., 2022) enable scalable high-resolution generation by operating on compressed representations, but this efficiency introduces an information bottleneck that discards fine-grained spatial details critical for faithful restoration. Recent analyses highlight a reconstruction–generation trade-off, where stronger compression benefits synthesis but degrades input fidelity (Yao et al., 2025). This issue is especially pronounced in SR, where subtle pixel-level structures must be preserved. Prior works mitigate it by strengthening conditioning or modifying inference (Wang et al., 2023b; Lin et al., 2024; Wang et al., 2023c), yet the underlying loss of pixel-domain information remains unresolved. Recent studies therefore revisit pixel-space modeling. Simple Diffusion (Hoogeboom et al., 2023) and Hourglass Diffusion Transformers (Crowson et al., 2024) show that pixel-space generation can scale with proper design, while JiT (Li and He, 2025) and Latent Forcing (Baade et al., 2026) further question the need for aggressive compression. These findings suggest that preserving or reintroducing pixel-space information is key to faithful reconstruction. Rather than discarding latent priors, our approach compensates for their information loss by reusing pre-VAE pixel evidence throughout restoration. Pixel-Guided and Grounded Super-Resolution. To mitigate fidelity loss, recent SR methods incorporate stronger conditioning into pretrained generative models. ControlNet (Zhang et al., 2023) enables spatially aligned conditioning and is widely used in restoration pipelines such as DiffBIR (Lin et al., 2024). Adapter-based methods, including T2I-Adapter (Mou et al., 2024) and LoRA (Hu et al., 2021), provide parameter-efficient task-specific guidance. More explicitly, pixel-aware SR methods aim to preserve local structures. PASD (Yang et al., 2024) and Pixel-aware Stable Diffusion (Yang et al., 2023) introduce pixel-level guidance into latent diffusion. SeeSR (Wu et al., 2023), FaithDiff (Chen et al., 2025), and GenDR (Wang et al., 2025) improve fidelity via semantic and structural conditioning. PiSA-SR (Sun et al., 2025) disentangles pixel fidelity and semantic enhancement with dual LoRA modules, while GuideSR (Arora et al., 2025) adds a full-resolution guidance branch. However, these methods typically treat pixel information as auxiliary to latent generation, leaving two issues: (1) latent trajectories may drift from LR structure, and (2) VAE decoding can further lose spatial detail. Our proposed Pixel-Grounded Super-Resolution (PGSR) addresses both issues by reusing pre-VAE pixel evidence at two stages: guiding the latent restoration trajectory and grounding the final VAE decoding. This dual design directly targets the information bottleneck of latent generative SR, enabling more faithful and consistent reconstruction. 3 Methodology In this section, we present PGSR as a pixel-grounded latent flow-matching framework for super-resolution. Instead of using the LR image only after VAE encoding, PGSR leverages pre-VAE pixel evidence to guide both latent trajectory formation and final rendering, addressing two fidelity gaps: VAE compression weakens LR structure, and the frozen decoder may lose spatial detail. As shown in Fig. 2, PGSR reuses pre-VAE pixel evidence at two stages via Pixel-Grounded Guidance: condition-side trajectory guidance anchors the latent flow to LR structure, while decoder-side grounding injects multi-scale cues into the frozen VAE decoder for faithful reconstruction. We first formulate latent flow-matching SR, then introduce shared pixel evidence with condition-side guidance and decoder-side grounding, followed by the learning objective and a parameter-efficient design. Figure 2: Overview of the training pipeline of PGSR. The LR observation is first aligned to the HR grid and encoded into a latent condition. PGSR introduces pixel-grounded evidence at two complementary locations: Condition-Side Trajectory Guidance fuses LR-derived pixel evidence with the latent condition to anchor the flow-matching trajectory, while Decoder-Side Pixel Grounding injects multi-scale pixel features into the frozen VAE decoder for faithful rendering. 3.1 Preliminaries on Latent Flow-Matching Super-Resolution Let xhr∈ℝH×W×3x_hr ^H× W× 3 be a high-resolution image and xlr∈ℝHs×Ws×3x_lr Hs× Ws× 3 its low-resolution observation under degradation D with scale s, i.e., xlr=(xhr)x_lr=D(x_hr). We upsample xlrx_lr to the HR grid, xlr↑=Bicubic(xlr)x_lr =Bicubic(x_lr), and encode both images with a frozen VAE: zlr=Evae(xlr↑),zhr=Evae(xhr).z_lr=E_vae(x_lr ), z_hr=E_vae(x_hr). We learn a conditional velocity predictor in latent space along the flow-matching trajectory. Given ϵ∼(0,I)ε (0,I) and noise level σt _t, zt=σtϵ+(1−σt)zhr,v⋆=ϵ−zhr.z_t= _tε+(1- _t)z_hr, v =ε-z_hr. The model predicts v v conditioned on the LR input and estimates z^0=zt−σtv^,ℒfm=‖v^−v⋆‖22. z_0=z_t- _t v, _fm=\| v-v \|_2^2. While efficient, this formulation conditions on the compressed latent zlrz_lr. We therefore introduce pixel grounding to preserve pre-VAE evidence and guide both the latent trajectory and final decoding. 3.2 Pixel-Grounded Super-Resolution Instead of being a global semantic context, PGSR keeps the LR observation available outside the VAE bottleneck by extracting pixel evidence before latent encoding. Pre-VAE pixel evidence. Given the upsampled LR image xlr↑x_lr , a lightweight pixel encoder P(⋅)P(·) produces a latent-resolution feature and multi-scale decoder features: (p¯lr,lr)=P(xlr↑),lr=s1,s2,s3. ( p_lr,S_lr )=P(x_lr ), _lr=\s_1,s_2,s_3\. Here p¯lr p_lr is used to ground the latent trajectory, while s1,s2,s3\s_1,s_2,s_3\ are used to ground the final VAE decoding process. This pixel evidence does not provide unobserved HR details; instead, it preserves LR-observed cues such as edges, boundaries, and local color transitions before they are compressed by the VAE. Condition-Side Trajectory Guidance. The latent LR condition zlrz_lr provides a compact structural anchor, while p¯lr p_lr supplies complementary pre-VAE image evidence. We fuse them through a gated residual correction: z~lr=zlr+λσ(g)Wp(p¯lr) z_lr=z_lr+λ\,σ(g)\,W_p( p_lr), where WpW_p is a 1×11× 1 projection, g is a learnable scalar gate, σ(⋅)σ(·) is the sigmoid function, and λ controls the pixel-conditioning strength. The grounded condition is then packed and passed to the ControlNet branch: Δt=Cϕ(Pack(zt),Pack(z~lr),t),v^=Fψ,ω(Pack(zt),t;Δt), _t=C_φ(Pack(z_t),Pack( z_lr),t), v=F_ψ,ω(Pack(z_t),t; _t), where Fψ,ωF_ψ,ω denotes the pretrained flow-matching transformer with frozen weights ψ and trainable LoRA parameters ω. Here Pack(⋅)Pack(·) denotes the standard rearrangement from latent feature maps to the image-token sequence consumed by the transformer. This grounds the latent trajectory without replacing the compact latent condition. Decoder-Side Pixel Grounding. Condition-Side Trajectory Guidance constrains the predicted latent, but the final image is still rendered by the frozen VAE decoder. To ground this decoding step, PGSR injects the multi-scale pixel features into matched decoder stages through decoder-side feature modulation (DFM). Let fdℓf_d denote the decoder activation before upsampling block ℓ . We apply f~dℓ=fdℓ+Zℓ(SiLU(Aℓ(sℓ))),ℓ∈0,1,2, f_d =f_d +Z_ (SiLU(A_ (s_ ))), ∈\0,1,2\, where sℓs_ denotes the scale-matched pixel tap (s3s_3 for ℓ=0 =0 at H/8H/8, s2s_2 for ℓ=1 =1 at H/4H/4, and s1s_1 for ℓ=2 =2 at H/2H/2), AℓA_ aligns the pixel feature to the decoder width, and ZℓZ_ is a zero-initialized output projection. The final prediction is obtained by x^hr=Dvaepg(z^0;lr). x_hr=D_vae^pg( z_0;S_lr). Here DvaepgD_vae^pg denotes the frozen VAE decoder equipped with DFM pixel-grounding adapters. Because ZℓZ_ is zero-initialized, the decoder is identical to the frozen VAE at initialization and DFM gradually learns pixel-grounded rendering during training. 3.3 Efficient Architecture Adaptation PGSR is a parameter-efficient adaptation of a pretrained latent flow-matching DiT. We freeze the latent autoencoder and generative backbone, and train only the ControlNet restoration branch, LoRA adapters, pre-VAE pixel encoder, gated trajectory-guidance fusion, and decoder-side pixel-grounding adapters. As SR is purely image-conditioned, we use cached empty-text embeddings and drive restoration solely from the LR input. For high-resolution efficiency, we adopt local-window attention by replacing dense image-token attention in selected blocks with pretrained local processors: Attn(qi)=∑j∈(i)∪αijvj,Attn(q_i)= _j (i) _ijv_j, where (i)N(i) is a local neighborhood and G optional global tokens. PGSR is fine-tuned on this accelerated backbone with the same grounding pathway and objective. The training objective combines latent flow supervision with pixel-grounded fidelity: ℒ=ℒfm+λpercℒperc+λpgℒpg,L=L_fm+ _percL_perc+ _pgL_pg, where ℒfmL_fm is the flow-matching loss. Image-space terms are computed from x^hr x_hr: ℒperc=mpercℒLPIPS(x^hr,xhr),ℒpg=1∑imi∑imi‖x^hr(i)−xhr(i)‖1.L_perc=m_perc\,L_LPIPS( x_hr,x_hr), _pg= 1 _im_i _im_i\| x_hr^(i)-x_hr^(i)\|_1. Here mi=[σi≤τ]m_i=1[ _i≤τ] is a low-noise mask, with mpercm_perc as its perceptual gate. Image-space supervision is applied only at low noise, where z^0=zt−σtv z_0=z_t- _t v is stable. Thus, ℒfmL_fm guides the full trajectory, while ℒpercL_perc and ℒpgL_pg refine reliable pixel-grounded outputs. 4 Experiments Datasets. We use two groups of training datasets and three evaluation benchmarks. For clean paired pretraining, we use DF2K, which combines DIV2K (Agustsson and Timofte, 2017) and Flickr2K (Wang et al., 2018), with paired bicubic ×4× 4 LR–HR images. For real-degradation adaptation, we construct a larger mixed HR corpus from the union of DF2K, LSDIR (Li et al., 2023), FFHQ (Karras et al., 2019), and OST (Wang et al., 2018); LR inputs are synthesized online with a real-world degradation pipeline. For evaluation, we report results on DIV2K validation (Agustsson and Timofte, 2017), RealSR (Cai et al., 2019), and DRealSR (Wei et al., 2020), covering both virtual bicubic degradation and real captured LR–HR pairs. Training and inference. We instantiate PGSR with FLUX.1-dev (Black Forest Labs, 2024) and initialize the restoration control branch from a pretrained SR ControlNet compatible with the base flow-matching model (Zhang et al., 2023). Stage 1 learns the clean SR mapping on DF2K and selects the best checkpoint by DIV2K validation PSNR. Stage 2 fine-tunes from this checkpoint on the mixed HR corpus using the second-order RealESRGAN degradation process (Wang et al., 2021), switches validation to real-world data, and selects the main model by RealSR validation LPIPS. In this stage, we enable the decoder-side DFM branch and the low-noise image-space losses while continuing to train the condition-side trajectory guidance modules. At inference time, PGSR follows the pretrained flow-matching sampling trajectory conditioned on the LR observation. Given the LR latent zlrz_lr and Gaussian noise ϵε, the initial latent is formed as zt0init=σt0ϵ+(1−σt0)zlrz_t_0^init= _t_0ε+(1- _t_0)z_lr, where t0t_0 controls how strongly the sampler departs from the LR latent condition. Unless otherwise specified, we use the full restoration trajectory and decode the final latent with the DFM-enabled VAE decoder. Evaluation metrics. We evaluate distortion fidelity with PSNR and SSIM (Wang et al., 2004), reference-based perceptual quality with LPIPS (Zhang et al., 2018a) and DISTS (Ding et al., 2022), and distribution-level fidelity with FID (Heusel et al., 2017). We further report no-reference perceptual metrics, including NIQE (Mittal et al., 2013), MUSIQ (Ke et al., 2021), MANIQA (Yang et al., 2022), and CLIP-IQA (Wang et al., 2023a). Higher is better for PSNR, SSIM, MUSIQ, MANIQA, and CLIP-IQA; lower is better for LPIPS, DISTS, FID, and NIQE. Implementation details. All experiments are conducted on 8 NVIDIA RTX 6000 Ada GPUs, each with 48GB of memory. Training uses bf16 mixed precision and distributed data parallelism via Hugging Face Accelerate. The VAE and pretrained FLUX backbone are frozen; the trainable components are the ControlNet branch, the shared pixel feature extractor, the condition-side trajectory guidance fusion layer, the decoder-side DFM adapters, and FLUX LoRA adapters. We optimize with AdamW using cosine learning-rate decay and linear warmup. Additional training, adaptation, degradation, and inference details are provided in Appendix A. Method RMSE↓ PSNR↑ SSIM↑ GT 0.00 ∞ 1.0000 SD VAE 14.42 24.95 0.8454 FLUX VAE 13.77 25.35 0.8528 Figure 3: VAE reconstruction stress test on an example. Left: visual comparison under controlled latent reconstruction. Right: quantitative reconstruction metrics. Both Stable Diffusion VAE and FLUX VAE exhibit substantial information loss due to latent compression, leading not only to blurring but also to severe structural degradation, where characters, digits, and fine patterns become largely unreadable or distorted beyond recognition. Necessity of pixel-level information for decoder-side grounding. We conduct a controlled VAE reconstruction experiment to analyze the fidelity of latent compression in standard encoder-decoder pipelines. Specifically, we feed ground-truth HR images into the VAE and reconstruct them via the standard encode-decode process, using both the Stable Diffusion VAE (Rombach et al., 2022) and FLUX VAE (Black Forest Labs, 2024). As shown in Fig. 3, both models exhibit noticeable reconstruction degradation, including distorted patterns and blurred fine-grained details, indicating that the VAE bottleneck is inherently lossy even under perfect input conditions. This suggests that encoder-decoder-based SR pipelines do not fully preserve or utilize pixel-level signals during reconstruction, resulting in unavoidable degradation of high-frequency content. These results highlight an important limitation of latent compression in existing generative SR systems: important spatial details are partially discarded during encoding, and cannot be fully recovered by the decoder alone. 4.1 Comparison with State-of-the-Art Methods Compared methods. We compare PGSR with representative generative SR methods which are reproducible, including ResShift (Yue et al., 2023), StableSR (Wang et al., 2023b), DiffBIR (Lin et al., 2024), SeeSR (Wu et al., 2023), PASD (Yang et al., 2024), OSEDiff (Wu et al., 2024), SinSR (Wang et al., 2023c), and PiSA-SR (Sun et al., 2025). Figure 4: Qualitative comparison on representative ×4× 4 SR examples from both virtual bicubic degradation and real degradation. PGSR aims to preserve LR-consistent structures while recovering perceptually plausible high-frequency details (i.e., correct flower details & text characters). Qualitative comparisons. Figure 4 shows representative visual comparisons on both virtual bicubic and real-degradation benchmarks. Compared with prior generative SR methods, PGSR is designed to preserve LR-consistent structures while recovering plausible high-frequency details, especially around repeated textures and small semantic regions. For example, the first row presents a penguin image from the DIV2K-Val dataset with virtual bicubic degradation, where the competing methods either produce overly sharp hair and hallucinated eye details or change the saturation of the image. In contrast, PGSR better preserves the spatial layout inherited from the LR input while producing sharp local details, leading to a more consistent result with the ground-truth. The second row shows a RealSR captured image, where the degradation is real-world degradation rather than a simple bicubic downsampling process. Several baselines, such as StableSR and DiffBIR, hallucinate textures or distort small structures under this real-world degradation, whereas PGSR maintains more faithful object boundaries with fewer artifacts; for example, PGSR correctly renders the text in the figure. Table 1: Quantitative comparison with representative generative SR methods on synthetic and real-world ×4× 4 benchmarks. All methods are evaluated using the same local metric pipeline, covering distortion metrics, full-reference perceptual metrics, distribution-level fidelity, and no-reference perceptual quality. For each dataset and metric, the best, second-best, and third-best results are highlighted in bold, underline, and italics, respectively. Dataset Method PSNR↑ SSIM↑ LPIPS↓ DISTS↓ FID↓ NIQE↓ MUSIQ↑ MANIQA↑ CLIP-IQA↑ DIV2K-Val ResShift 25.56 0.7625 0.2166 0.0797 28.36 4.8223 62.74 0.3555 0.6276 StableSR 23.55 0.7050 0.2272 0.0850 32.50 3.7174 68.55 0.4591 0.7080 DiffBIR 23.04 0.6852 0.2731 0.1054 36.48 3.6071 68.06 0.4639 0.7370 SeeSR 25.51 0.7566 0.2225 0.0866 31.19 3.8600 67.11 0.4340 0.6403 PASD 24.86 0.7373 0.2361 0.0849 29.94 3.3494 66.66 0.3975 0.5996 OSEDiff 23.16 0.7058 0.2386 0.1031 34.30 3.4451 69.34 0.4404 0.7004 SinSR 25.78 0.7781 0.2107 0.0862 27.39 4.2933 64.58 0.3881 0.6582 PiSA-SR 23.59 0.7087 0.2158 0.0937 32.71 3.2426 70.46 0.4556 0.7190 PGSR (ours) 25.89 0.7707 0.2104 0.0792 24.88 3.2244 67.93 0.3913 0.6479 DRealSR ResShift 24.73 0.6702 0.4298 0.1078 54.11 6.6914 31.91 0.3060 0.6069 StableSR 24.77 0.6934 0.4194 0.1116 55.07 4.5860 34.78 0.4094 0.6720 DiffBIR 24.83 0.5979 0.4582 0.1255 54.30 4.6915 34.75 0.4132 0.6890 SeeSR 25.91 0.7755 0.2761 0.0962 46.91 5.3388 33.33 0.3606 0.5459 PASD 25.84 0.7464 0.2898 0.1087 50.28 6.2480 29.54 0.3194 0.4442 OSEDiff 24.69 0.7358 0.3244 0.1117 46.61 4.1527 37.01 0.4764 0.7016 SinSR 25.47 0.6632 0.4496 0.1047 60.62 5.7972 31.33 0.3590 0.6937 PiSA-SR 25.37 0.7592 0.3133 0.1142 49.88 4.4010 34.67 0.4456 0.7171 PGSR (ours) 25.97 0.7550 0.3054 0.0911 46.15 3.8707 35.83 0.3144 0.5932 RealSR ResShift 24.06 0.7112 0.3491 0.1758 63.61 6.9271 55.20 0.3336 0.5647 StableSR 22.77 0.6974 0.3288 0.1748 63.08 5.0611 62.57 0.4446 0.6284 DiffBIR 23.74 0.6353 0.3456 0.1807 59.47 4.9181 62.51 0.4700 0.6958 SeeSR 25.13 0.7620 0.2750 0.1553 61.99 5.3505 61.20 0.4380 0.5984 PASD 25.20 0.7477 0.2737 0.1473 52.85 4.8421 58.48 0.3741 0.5182 OSEDiff 23.68 0.7163 0.2999 0.1609 58.80 4.3153 67.29 0.4758 0.6832 SinSR 24.72 0.7080 0.3642 0.1766 67.05 5.8306 57.86 0.3844 0.6405 PiSA-SR 24.03 0.7307 0.2719 0.1564 61.42 4.3685 67.97 0.4746 0.6745 PGSR (ours) 24.75 0.7495 0.2596 0.1365 54.63 4.0470 63.39 0.4116 0.5593 Table 2: Architecture ablation of pixel-grounded pathways in PGSR. The left table reports quantitative results on DIV2K-Val and RealSR, while the right panel shows a representative visual ablation. Removing either the condition-side trajectory guidance or the decoder-side grounding degrades reconstruction and perceptual quality, and the full design gives the best results on both datasets. Dataset Variant PSNR↑ SSIM↑ LPIPS↓ DIV2K-Val w/o Pixel-Grounded Guidance 23.68 0.7592 0.2431 w/o Condition-Side Guidance 24.66 0.7644 0.2204 w/o Decoder-Side Grounding 24.78 0.7651 0.2188 PGSR (full) 25.89 0.7707 0.2104 RealSR w/o Pixel-Grounded Guidance 22.15 0.7305 0.2789 w/o Condition-Side Guidance 24.22 0.7420 0.2631 w/o Decoder-Side Grounding 24.08 0.7401 0.2626 PGSR (full) 24.75 0.7495 0.2596 Quantitative comparisons. Table 1 reports quantitative comparisons on synthetic and real-world ×4× 4 SR benchmarks using distortion, perceptual, distribution-level, and no-reference quality metrics. On DIV2K-Val, PGSR achieves the best PSNR, LPIPS, DISTS, FID, and NIQE, and ranks second in SSIM, indicating that preserving pre-VAE pixel evidence improves fidelity to the LR observation while maintaining strong perceptual quality. Notably, compared with perception-oriented methods such as DiffBIR and PiSA-SR, PGSR obtains substantially better distortion and perceptual metrics, suggesting that Pixel-Grounded Guidance reduces visually plausible but input-inconsistent hallucinations. On DRealSR, PGSR obtains the best PSNR, DISTS, FID, and NIQE, showing strong robustness to real-world degradations and degradation traces. On RealSR, PGSR achieves the best LPIPS, DISTS, and NIQE, and ranks second in SSIM and FID. These results demonstrate a favorable realism–fidelity trade-off across both synthetic and real settings: the latent flow-matching backbone provides realistic textures, while trajectory guidance and decoder-side grounding constrain the restoration with LR-observed pixel evidence during latent generation and final rendering. 4.2 Ablation Study Ablation study on PGSR components. We ablate the architectural contribution of the two pixel-grounded pathways in Table 2. Removing Pixel-Grounded Guidance leads to the largest degradation, confirming the importance of preserving pre-VAE pixel evidence for faithful generative SR. When either pathway is removed, performance consistently drops across PSNR, SSIM, and LPIPS, showing that our design provides complementary benefits. The full PGSR model achieves the best results on both datasets, validating the effectiveness of jointly grounding the latent trajectory and the final rendering. The loss-component ablation is complementary and is deferred to Appendix B.2. Impact of Sparse Attention. We further evaluate a sparse local-attention variant that replaces selected dense image-token attention processors with pretrained local-window attention. As shown in Table 3, this acceleration mainly affects computational efficiency while preserving the effectiveness of Pixel-Grounded Guidance. Compared with the standard PGSR backbone, sparse attention substantially reduces inference cost while only slightly degrading restoration quality, indicating that the proposed trajectory guidance and decoder-side grounding are compatible with efficient attention backbones. The incorporation of sparse attention also enables us to perform super-resolution from 2K to 8K; the results are shown in Figure 5. Table 3: Efficiency-quality comparison between standard and Sparse Attention-accelerated PGSR inference. Inference time is measured per image and per denoising step. Dataset Variant Resolution Efficiency Quality Time (s/img)↓ Time (s/step)↓ PSNR↑ SSIM↑ LPIPS↓ DIV2K-Val PGSR w/o Sparse Attention 1792×17921792×1792 61.81 3.09 26.36 0.7710 0.2571 PGSR + Sparse Attention 1792×17921792×1792 38.95 1.95 25.81 0.7679 0.2603 RealSR PGSR w/o Sparse Attention 1536×15361536×1536 58.28 2.91 24.88 0.7501 0.2582 PGSR + Sparse Attention 1536×15361536×1536 37.09 1.85 24.37 0.7482 0.2601 Figure 5: 8K Super-resolution demo using our method. The super-resolution results demonstrate clear quality improvements over the LR input on the DIV8K dataset. Limitations. PGSR inherits both the strengths and costs of large pretrained flow-matching models. Due to the large ControlNet and the backbone, training requires substantial memory, and inference remains slower than one-step SR models. Besides, since our losses emphasize LR consistency and a mean-error learning objective, PGSR can produce slightly smoother textures than methods that aggressively optimize perceptual sharpness. This reflects a realism–fidelity trade-off; future work may improve sharpness through distillation while preserving input-output consistency. 5 Conclusion We presented PGSR, a generative super-resolution framework centered on Pixel-Grounded Guidance. Rather than treating the LR image only as a latent condition, PGSR reuses pre-VAE pixel evidence through two complementary mechanisms: Condition-Side Trajectory Guidance anchors the ControlNet condition and latent flow trajectory, while Decoder-Side Pixel Grounding injects multi-scale pixel evidence into the frozen VAE decoder. This dual design directly addresses the fidelity loss caused by latent compression and provides a practical path toward more faithful generative SR with large pretrained diffusion transformers. References E. Agustsson and R. Timofte (2017) NTIRE 2017 challenge on single image super-resolution: dataset and study. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, Cited by: §4. A. Arora, Z. Tu, Y. Wang, R. Bai, J. Wang, and S. Ma (2025) GuideSR: rethinking guidance for one-step high-fidelity diffusion-based super-resolution. In Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops, Cited by: §1, §2. A. Baade, E. R. Chan, K. Sargent, C. Chen, J. Johnson, E. Adeli, and L. Fei-Fei (2026) Latent forcing: reordering the diffusion trajectory for pixel-space image generation. arXiv preprint arXiv:2602.11401. Cited by: §2. Black Forest Labs (2024) FLUX. External Links: Link Cited by: §4, §4. Y. Blau and T. Michaeli (2018) The perception-distortion tradeoff. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §2. J. Cai, H. Zeng, H. Yong, Z. Cao, and L. Zhang (2019) Toward real-world single image super-resolution: a new benchmark and a new model. In IEEE/CVF International Conference on Computer Vision (ICCV), Cited by: §4. K. C. K. Chan, X. Wang, X. Xu, J. Gu, and C. C. Loy (2021) GLEAN: generative latent bank for large-factor image super-resolution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §2. J. Chen, J. Pan, and J. Dong (2025) FaithDiff: unleashing diffusion priors for faithful image super-resolution. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 28188–28197. Cited by: §2. K. Crowson, S. A. Baumann, A. Birch, T. M. Abraham, D. Z. Kaplan, and E. Shippole (2024) Scalable high-resolution pixel-space image synthesis with hourglass diffusion transformers. In Proceedings of the 41st International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 235, p. 9550–9575. Cited by: §2. K. Ding, K. Ma, S. Wang, and E. P. Simoncelli (2022) Image quality assessment: unifying structure and texture similarity. IEEE Transactions on Pattern Analysis and Machine Intelligence 44 (5), p. 2567–2581. Cited by: §4. C. Dong, C. C. Loy, K. He, and X. Tang (2014) Learning a deep convolutional network for image super-resolution. In European Conference on Computer Vision (ECCV), Cited by: §2. M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochreiter (2017) GANs trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems 30. Cited by: §4. E. Hoogeboom, J. Heek, and T. Salimans (2023) Simple diffusion: end-to-end diffusion for high resolution images. In Proceedings of the 40th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 202, p. 13240–13258. Cited by: §2. E. J. Hu, Y. Shen, P. Wallis, Z. Allen-Zhu, Y. Li, S. Wang, L. Wang, and W. Chen (2021) LoRA: low-rank adaptation of large language models. arXiv preprint arXiv:2106.09685. Cited by: §2. J. Johnson, A. Alahi, and L. Fei-Fei (2016) Perceptual losses for real-time style transfer and super-resolution. In European Conference on Computer Vision (ECCV), Cited by: §2. T. Karras, S. Laine, and T. Aila (2019) A style-based generator architecture for generative adversarial networks. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 4401–4410. Cited by: §4. B. Kawar, M. Elad, S. Ermon, and J. Song (2022) Denoising diffusion restoration models. In Advances in neural information processing systems (NeurIPS), Cited by: §2. J. Ke, Q. Wang, Y. Wang, P. Milanfar, and F. Yang (2021) MUSIQ: multi-scale image quality transformer. In IEEE/CVF International Conference on Computer Vision (ICCV), p. 5148–5157. Cited by: §4. J. Kim, J. K. Lee, and K. M. Lee (2016) Accurate image super-resolution using very deep convolutional networks. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §2. D. P. Kingma and M. Welling (2014) Auto-encoding variational bayes. In International Conference on Learning Representations (ICLR), Cited by: §1. C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi (2017) Photo-realistic single image super-resolution using a generative adversarial network. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §1, §2. J. Li, J. Cao, Y. Guo, W. Li, and Y. Zhang (2025) One diffusion step to real-world super-resolution via flow trajectory distillation. In International Conference on Machine Learning (ICML), p. 34044–34053. Cited by: §2. T. Li and K. He (2025) Back to basics: let denoising generative models denoise. arXiv preprint arXiv:2511.13720. Cited by: §2. Y. Li, K. Zhang, J. Liang, J. Cao, C. Liu, R. Gong, Y. Zhang, H. Tang, Y. Liu, D. Demandolx, R. Ranjan, R. Timofte, and L. Van Gool (2023) LSDIR: a large scale dataset for image restoration. In IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), p. 1775–1787. Cited by: §4. J. Liang, J. Cao, G. Sun, K. Zhang, L. Van Gool, and R. Timofte (2021) SwinIR: image restoration using swin transformer. In IEEE/CVF International Conference on Computer Vision Workshops, Cited by: §2. X. Lin, J. He, Z. Chen, Z. Lyu, B. Dai, F. Yu, W. Ouyang, Y. Qiao, and C. Dong (2024) DiffBIR: towards blind image restoration with generative diffusion prior. In European Conference on Computer Vision (ECCV), Cited by: §2, §2, §2, §4.1. A. Mittal, R. Soundararajan, and A. C. Bovik (2013) Making a “completely blind” image quality analyzer. IEEE Signal Processing Letters 20 (3), p. 209–212. Cited by: §4. C. Mou, X. Wang, L. Xie, J. Zhang, Z. Qi, Y. Shan, and X. Qie (2024) T2I-adapter: learning adapters to dig out more controllable ability for text-to-image diffusion models. In Proceedings of the AAAI Conference on Artificial Intelligence, Cited by: §2. Y. Qu, K. Yuan, K. Zhao, Q. Xie, J. Hao, M. Sun, and C. Zhou (2024) XPSR: cross-modal priors for diffusion-based image super-resolution. In European Conference on Computer Vision (ECCV), Cited by: §2. R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer (2022) High-resolution image synthesis with latent diffusion models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §1, §2, §4. C. Saharia, J. Ho, W. Chan, T. Salimans, D. J. Fleet, and M. Norouzi (2021) Image super-resolution via iterative refinement. arXiv preprint arXiv:2104.07636. Cited by: §1, §2. L. Sun, R. Wu, Z. Ma, S. Liu, Q. Yi, and L. Zhang (2025) Pixel-level and semantic-level adjustable super-resolution: a dual-lora approach. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §1, §2, §4.1. J. Wang, K. C. K. Chan, and C. C. Loy (2023a) Exploring clip for assessing the look and feel of images. Proceedings of the AAAI Conference on Artificial Intelligence 37 (2), p. 2555–2563. Cited by: §4. J. Wang, Z. Yue, S. Zhou, K. C. K. Chan, and C. C. Loy (2023b) Exploiting diffusion prior for real-world image super-resolution. arXiv preprint arXiv:2305.07015. Cited by: §1, §2, §2, §4.1. X. Wang, L. Xie, C. Dong, and Y. Shan (2021) Real-esrgan: training real-world blind super-resolution with pure synthetic data. arXiv preprint arXiv:2107.10833. Cited by: §2, §4. X. Wang, K. Yu, S. Wu, J. Gu, Y. Liu, C. Dong, Y. Qiao, and C. Change Loy (2018) ESRGAN: enhanced super-resolution generative adversarial networks. arXiv preprint arXiv:1809.00219. Cited by: §1, §2, §4. Y. Wang, S. Zhao, K. Zhang, J. Li, and L. Zhang (2025) GenDR: lighten generative detail restoration. arXiv preprint arXiv:2503.06790. Cited by: §2. Y. Wang, W. Yang, X. Chen, Y. Wang, L. Guo, L. Chau, Z. Liu, Y. Qiao, A. C. Kot, and B. Wen (2023c) SinSR: diffusion-based image super-resolution in a single step. arXiv preprint arXiv:2311.14760. Cited by: §2, §2, §4.1. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli (2004) Image quality assessment: from error visibility to structural similarity. IEEE TIP. Cited by: §2, §4. P. Wei, H. Lu, H. Liu, F. Zhu, C. Zhao, S. Xu, and B. Zeng (2020) Component divide-and-conquer for real-world image super-resolution. In European Conference on Computer Vision (ECCV), Cited by: §4. R. Wu, L. Sun, Z. Ma, and L. Zhang (2024) One-step effective diffusion network for real-world image super-resolution. In Neural Information Processing Systems (NeurIPS), Cited by: §2, §4.1. R. Wu, T. Yang, L. Sun, Z. Zhang, S. Li, and L. Zhang (2023) SeeSR: towards semantics-aware real-world image super-resolution. arXiv preprint arXiv:2311.16518. Cited by: §1, §1, §2, §2, §4.1. J. Xu, W. Li, H. Sun, F. Li, Z. Wang, L. Peng, J. Ren, H. Yang, X. Hu, R. Pei, and P. Heng (2025) Fast image super-resolution via consistency rectified flow. In IEEE/CVF International Conference on Computer Vision (ICCV), p. 11755–11765. Cited by: §2. S. Yang, T. Wu, S. Shi, S. Lao, Y. Gong, M. Cao, J. Wang, and Y. Yang (2022) MANIQA: multi-dimension attention network for no-reference image quality assessment. In IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), p. 1191–1200. Cited by: §4. T. Yang, R. Wu, P. Ren, X. Xie, and L. Zhang (2023) Pixel-aware stable diffusion for realistic image super-resolution. arXiv preprint arXiv:2308.14469. Cited by: §2. T. Yang, R. Wu, P. Ren, X. Xie, and L. Zhang (2024) Pixel-aware stable diffusion for realistic image super-resolution and personalized stylization. In European Conference on Computer Vision (ECCV), Cited by: §1, §2, §4.1. J. Yao, B. Yang, and X. Wang (2025) Reconstruction vs. generation: taming optimization dilemma in latent diffusion models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §2. Z. Yue, J. Wang, and C. C. Loy (2023) ResShift: efficient diffusion model for image super-resolution by residual shifting. arXiv preprint arXiv:2307.12348. Cited by: §2, §4.1. K. Zhang, J. Liang, L. Van Gool, and R. Timofte (2021) Designing a practical degradation model for deep blind image super-resolution. arXiv preprint arXiv:2103.14006. Cited by: §2. L. Zhang, A. Rao, and M. Agrawala (2023) Adding conditional control to text-to-image diffusion models. In IEEE/CVF International Conference on Computer Vision (ICCV), Cited by: §1, §2, §4. R. Zhang, P. Isola, A. A. Efros, E. Shechtman, and O. Wang (2018a) The unreasonable effectiveness of deep features as a perceptual metric. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §4. R. Zhang, P. Isola, A. Efros, E. Shechtman, and O. Wang (2018b) The unreasonable effectiveness of deep features as a perceptual metric. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Cited by: §2. Appendix A Additional Implementation Details We provide additional implementation details to facilitate reproducibility. Unless otherwise stated, all reported PGSR models are initialized from black-forest-labs/FLUX.1-dev. The restoration ControlNet branch is initialized from a FLUX-compatible SR ControlNet checkpoint, while the FLUX backbone and the VAE encoder–decoder remain frozen throughout training. The trainable components include the ControlNet restoration branch, the pre-VAE pixel extractor, the gated condition-side pixel fusion layer, decoder-side DFM adapters, and LoRA adapters inserted into the FLUX backbone. Optimization. We train PGSR with AdamW using a base learning rate of 1×10−51× 10^-5, weight decay 0.010.01, and Adam coefficients (β1,β2)=(0.9,0.999)( _1, _2)=(0.9,0.999). The learning rate is linearly warmed up for the first 5 epochs and then decayed with a cosine schedule. The ControlNet branch uses the base learning rate, while the pixel branch and LoRA parameters use a higher learning rate of 1×10−41× 10^-4. Training is performed with bfloat16 mixed precision on 8 NVIDIA RTX 6000 Ada GPUs. Unless otherwise specified, we use a per-GPU batch size of 4 and gradient accumulation of 8, resulting in an effective batch size of 256. We use a fixed random seed of 42 for the reported runs. Training protocol. For the clean paired stage, we train on DF2K with paired bicubic ×4× 4 LR–HR images. HR crops of size 512×512512× 512 are used, corresponding to 128×128128× 128 LR crops for ×4× 4 SR. We sample two crops per image and train for 60 epochs. The clean-stage checkpoint is selected according to DIV2K validation PSNR. For the real-world degradation stage, we fine-tune the clean checkpoint using a Real-ESRGAN-style second-order degradation process on the mixed HR corpus described in Sec. 4. The real-world stage uses validation on real captured data, and the checkpoint used for the main real-world results is selected according to RealSR validation LPIPS. Model adaptation. The condition-side pixel feature is fused with the LR latent condition through the gated residual formulation described in Sec. 3.2. The pixel gate is initialized with a positive logit, so that pixel evidence is active at the beginning of training while still being learnable. LoRA adapters use rank 16, alpha 16, zero dropout, and Gaussian initialization. Since SR is fully image-conditioned, we use cached empty-text embeddings during training and inference. In our implementation, we additionally allow a small set of learnable leading text tokens with a substantially smaller learning rate and L2 regularization; this component is used only as a lightweight prior adapter and is not the main source of image conditioning. Decoder-side pixel grounding. The decoder-side DFM branch is enabled for the full PGSR model. Multi-scale pixel features are injected into the frozen VAE decoder at three matched resolutions: the deepest pixel tap is injected into the first upsampling stage, the intermediate tap into the second stage, and the shallowest tap into the third stage. The pixel extractor uses progressively wider channels across scales, and the latent-resolution pixel feature is projected to match the latent conditioning width before gated fusion. For image-space supervision, we apply the low-noise gating described in Sec. 3.3, so that pixel and perceptual losses are only applied when the predicted clean latent is sufficiently stable. Degradation settings. In the clean paired stage, the model is trained with paired bicubic ×4× 4 LR–HR data rather than online real-world degradation. In the real-world stage, we use a second-order degradation pipeline following Real-ESRGAN. The pipeline includes stochastic blur, resizing, Gaussian or Poisson noise, JPEG compression, optional second degradation, final sinc filtering, and unsharp masking of the HR target. We use this stage to expose PGSR to realistic blur–noise–compression artifacts while preserving the same pixel-grounded architecture. Inference. Unless otherwise specified, PGSR uses 20 denoising steps at inference time. We use 20 denoising steps and set the denoising strength to 1.0, i.e., sampling starts from the noisiest restoration state and follows the full restoration trajectory. The final latent prediction is decoded with the DFM-enabled VAE decoder. For large images, we use tiled evaluation with a default tile size of 512 and overlap of 64 to reduce memory usage while avoiding visible boundary artifacts. Appendix B Supplementary Experiments Figure 6: Additional qualitative comparison on real degradation. Figure 7: Additional qualitative comparison on synthetic degradation. B.1 Additional Visual Comparisons We provide additional qualitative comparisons on RealSR, DRealSR, and DIV2K-Val in Figs. 6–7. These examples complement the main-text visualization by covering more diverse textures, structures, and real-world degradations. B.2 Additional Ablation Tables In this section, we present additional ablation studies on key hyperparameters and loss components. Table 4 studies the most relevant training-time hyperparameters around the final Stage-2 recipe. We vary the perceptual loss weight λperc _perc, the pixel-grounded reconstruction weight λpg _pg, and the pixel-conditioning strength spcs_pc. Here spcs_pc scales the condition-side pixel evidence before it is fused into the LR latent condition; it is a conditioning strength and is distinct from the LR-anchored sampling strength used at inference time, which controls the denoising start point. Other optimizer and engineering settings are kept in the released configuration files. Table 4: Sensitivity to the two image-space loss weights and the pixel-conditioning strength. Rows are grouped by the factor being swept; within each group, all other settings are fixed to the default Stage-2 recipe. We report PSNR and LPIPS to show the fidelity–perception effect of each hyperparameter. Sweep Variant λperc _perc λpg _pg spcs_pc DIV2K-Val RealSR PSNR↑ LPIPS↓ PSNR↑ LPIPS↓ Loss weights No image-space loss 0 0 1.0 24.46 0.2301 23.25 0.2784 Loss weights Perceptual only 0.05 0 1.0 24.68 0.2172 24.01 0.2635 Loss weights Weak pixel loss 0.05 0.025 1.0 25.06 0.2113 24.53 0.2619 Loss weights Default 0.05 0.05 1.0 25.89 0.2104 24.75 0.2596 Loss weights Strong pixel loss 0.05 0.10 1.0 25.83 0.2160 24.32 0.2655 Conditioning Weak pixel conditioning 0.05 0.05 0.8 26.01 0.2307 24.67 0.2706 Conditioning Strong pixel conditioning 0.05 0.05 1.2 25.42 0.2244 24.38 0.2664 Table 5 reports the loss-component ablation used to separate supervision effects from the architectural ablation in the main text. Starting from the latent flow-matching objective, adding perceptual supervision improves LPIPS on both DIV2K-Val and RealSR, while the pixel-grounded reconstruction loss further improves distortion metrics. We also test an optional perceptual term on the DFM-decoded prediction to examine whether the decoder-side pixel-grounding branch benefits from perceptual supervision in addition to pixel-wise reconstruction: ℒext=ℒfm+λpercℒperc+λpgℒpg+λpg-percℒpg-perc,ℒpg-perc=mpgℒLPIPS(x^hrDFM,xhr).L_ext=L_fm+ _percL_perc+ _pgL_pg+ _pg -percL_pg -perc, _pg -perc=m_pgL_LPIPS( x_hr^DFM,x_hr). Here x^hrDFM x_hr^DFM is decoded through the DFM path and mpgm_pg uses the same low-noise gate as ℒpgL_pg. The default PGSR recipe sets λpg-perc=0 _pg -perc=0; the final row is included only as an exploratory ablation of perceptual supervision inside the DFM branch. Table 5: Loss-component ablation of PGSR on DIV2K-Val and RealSR validation. Each row progressively adds one supervision term to the latent flow-matching baseline. The optional DFM perceptual term tests whether applying LPIPS directly on the DFM-decoded prediction further improves perceptual quality. Variant ℒfmL_fm ℒpercL_perc ℒpgL_pg ℒpg-percL_pg -perc DIV2K-Val RealSR PSNR↑ SSIM↑ LPIPS↓ PSNR↑ SSIM↑ LPIPS↓ FM control only ✓ – – – 24.67 0.7580 0.2431 22.15 0.7305 0.2789 + perceptual ✓ ✓ – – 24.78 0.7651 0.2188 24.08 0.7401 0.2626 PGSR (default) ✓ ✓ ✓ – 25.89 0.7707 0.2104 24.75 0.7495 0.2596 + DFM perceptual ✓ ✓ ✓ ✓ 25.70 0.7696 0.2102 24.36 0.7490 0.2588 Appendix C Supplementary Analytical Discussion This section provides additional analysis for the pixel-grounded components introduced in Sec. 3. The goal is not to establish global optimality, but to clarify the inductive biases behind the proposed design: gated residual condition fusion can attenuate unreliable pixel corrections while keeping the LR latent as an anchor, multi-scale pixel taps reduce the bottleneck imposed by a single flat pixel representation, and zero-initialized DFM preserves the frozen decoder before image-space supervision becomes reliable. C.1 Gated Residual Condition Fusion In Sec. 3, the condition-side fused latent is written as z~lr=zlr+λσ(g)Wp(p¯lr), z_lr=z_lr+λ\,σ(g)\,W_p( p_lr), where zlrz_lr is the VAE-encoded LR condition, p¯lr p_lr is the pre-VAE pixel feature projected to the latent resolution, WpW_p is a learned 1×11× 1 projection, g is a learnable scalar gate, and λ controls the strength of the pixel evidence. Proposition A.1. Assume that the ideal fused condition is zlr+δz_lr+δ, and the projected pixel correction is a noisy estimate Wp(p¯lr)=δ+ηW_p( p_lr)=δ+η with [η]=0E[η]=0 and ‖η‖22=νE\|η\|_2^2=ν. Among residual fusions of the form zlr+λγWp(p¯lr)z_lr+λγ W_p( p_lr) with γ∈[0,1]γ∈[0,1], the optimal gate is γ⋆=clip[0,1](‖δ‖22λ(‖δ‖22+ν)),γ =clip_[0,1] ( \|δ\|_2^2λ(\|δ\|_2^2+ν) ), and is no worse in expected squared error than any fixed additive choice when that fixed choice lies in the same interval. Proof. For a given γ, the expected error of the fused condition is ℰ(γ)=‖zlr+λγ(δ+η)−(zlr+δ)‖22=(1−λγ)2‖δ‖22+λ2γ2ν.E(γ)=E \|z_lr+λγ(δ+η)-(z_lr+δ) \|_2^2=(1-λγ)^2\|δ\|_2^2+λ^2γ^2ν. Minimizing this convex quadratic and projecting the minimizer onto [0,1][0,1] gives γ⋆γ . Since the gated family contains all fixed residual scales in [0,1][0,1], its best attainable error cannot be larger than that of direct addition with any such fixed scale. □ Discussion. This proposition should be read as a bias argument rather than a full optimization guarantee. The LR latent remains a stable residual anchor for the flow-matching trajectory, while the gate gives the model a simple mechanism to attenuate noisy pixel evidence under severe degradation. Compared with fixed additive fusion, gated residual fusion keeps the benefits of immediate pixel participation but avoids forcing every pixel correction to enter the latent condition with the same strength. C.2 Approximation Advantage of Multi-Scale Pixel Taps PGSR uses a three-stage pixel extractor that produces matched taps lr=s1,s2,s3S_lr=\s_1,s_2,s_3\ at H/2H/2, H/4H/4, and H/8H/8 resolutions. This design is motivated by the decoder-side use case. The frozen latent decoder reconstructs an HR image through multiple upsampling blocks, and each block operates at a different spatial scale. A flat extractor that outputs only one latent-resolution feature must predict corrections for all decoder stages from the same compressed representation. Let rℓr_ denote the ideal pixel correction for decoder stage ℓ . A flat extractor first maps the upsampled LR image into a single low-resolution feature q and then predicts each stage correction from q: q=B3xlr↑,r^ℓflat=UℓAℓq,q=B_3x_lr , r_ ^flat=U_ A_ q, where B3B_3 is the low-resolution pixel encoder, AℓA_ is a stage-specific projection, and UℓU_ upsamples the feature when required. The best achievable squared approximation error is ℰflat=minAℓ∑ℓ[‖rℓ−UℓAℓB3xlr↑‖22].E_flat= _\A_ \ _ E [ \|r_ -U_ A_ B_3x_lr \|_2^2 ]. By contrast, a multi-scale extractor predicts each correction from a matched feature tap: sℓ=Bℓxlr↑,r^ℓmulti=Aℓsℓ,s_ =B_ x_lr , r_ ^multi=A_ s_ , with approximation error ℰmulti=minAℓ,Bℓ∑ℓ[‖rℓ−AℓBℓxlr↑‖22].E_multi= _\A_ ,B_ \ _ E [ \|r_ -A_ B_ x_lr \|_2^2 ]. Proposition A.2. The multi-scale formulation is at least as expressive as the flat formulation: ℰmulti≤ℰflat.E_multi _flat. Proof. The multi-scale family can emulate any flat solution by choosing each BℓB_ to factor through the same low-resolution representation B3xlr↑B_3x_lr and absorbing the upsampling/projection into AℓA_ . Therefore, the hypothesis class optimized by ℰflatE_flat is a subset of the hypothesis class optimized by ℰmultiE_multi. Minimizing over a superset cannot yield a larger minimum error, which gives ℰmulti≤ℰflatE_multi _flat. □ Discussion. This result should be interpreted as an approximation-capacity argument rather than a guarantee of better test performance. It supports the architectural choice of feeding DFM with scale-matched taps: high-frequency LR-observed cues may be attenuated by a latent-resolution bottleneck, and later projections cannot recover information that has already been discarded. Providing s1s_1, s2s_2, and s3s_3 gives the decoder access to pixel evidence at the same scales where details are rendered. C.3 Identity Property of Decoder-Side DFM For decoder stage ℓ , the DFM adapter applies f~dℓ=fdℓ+Zℓ(SiLU(Aℓ(sℓ))), f_d =f_d +Z_ \! (SiLU(A_ (s_ )) ), where fdℓf_d is the frozen decoder activation, sℓs_ is the matched pixel feature tap, AℓA_ aligns channel width, and ZℓZ_ is a zero-initialized output projection. Proposition A.3. If ZℓZ_ is zero-initialized, then DFM preserves the frozen decoder at initialization: f~dℓ=fdℓfor every decoder stage ℓ. f_d =f_d for every decoder stage . Proof. Since ZℓZ_ is zero-initialized, Zℓ(SiLU(Aℓ(sℓ)))=0Z_ \! (SiLU(A_ (s_ )) )=0 at initialization for any input feature sℓs_ . Therefore, f~dℓ=fdℓ+0=fdℓ. f_d =f_d +0=f_d . □ Discussion. The DFM-enhanced decoder starts exactly as the frozen VAE decoder and gradually learns pixel-grounded rendering only when image-space supervision provides a useful signal. This is important because the decoder is a pretrained component: without an identity-preserving initialization, injected pixel modulation could perturb decoder activations before the adapters learn meaningful spatial corrections.