GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance

Conference: ICML 2026
arXiv: 2606.03119
Code: TBD
Area: Image Generation / Diffusion Bridge / Guidance
Keywords: bridge model, prior guidance, frequency modulation, image translation, training-free

TL;DR

Addressing diffusion bridge models (data-to-data generation), this paper proposes a training-free Prior Guidance (PG). By perturbing a clean prior to construct a "weak prior" and extrapolating between the denoising results of strong and weak priors, the model's utilization of the prior is amplified. Further utilizing U-shaped Frequency Modulation (FMPG) and a cascaded CFG-FMPG framework, the method stably improves the FID of pre-trained bridge models like DDBM/DBIM across tasks such as Edges→Handbags, DIODE, and ImageNet inpainting without additional training or increased NFE.

Background & Motivation

Background: Guidance for Diffusion has matured into two major paradigms: CFG, which uses "conditional vs. unconditional" denoising results for extrapolation to enhance conditional alignment, and AG, which uses "well-trained vs. under-trained" denoising results for extrapolation to improve score accuracy. Both essentially "create a quality gap between two denoising steps and extrapolate towards the higher quality direction." Meanwhile, bridge models (DDBM, DBIM, I2SB, etc.) transform the generation process into data-to-data by conditioning on a clean prior \(\bm{x}_T\), proving more efficient than diffusion from pure Gaussian noise for tasks with strong priors like image-to-image translation and restoration.

Limitations of Prior Work: While CFG/AG can be directly ported to bridge models, they fail to utilize the fundamental difference between bridges and diffusion—prior exploitation (the utilization of the clean prior provided by \(\bm{x}_T\)). In other words, ported guidance only "strengthens conditions" or "corrects score errors" without specifically reinforcing whether the model truly fully utilizes the prior. Furthermore, AG requires training an additional under-trained network, which is costly.

Key Challenge: The greatest advantage of bridge models over diffusion lacks a corresponding guidance design. Moreover, the SNR of bridge models follows a U-shaped trajectory (clean at both ends, noisiest in the middle), which differs significantly from the monotonically increasing SNR of diffusion. Consequently, applying a constant guidance scale across all timesteps and frequency bands ignores the bridge's inherent geometric structure.

Goal: (1) Design the first training-free guidance specifically for bridge models, mapping the guidance signal directly to "prior exploitation"; (2) Match the guidance intensity to the U-shaped SNR and frequency behavior of the bridge; (3) Ensure the method remains applicable even when the prior itself is weak (e.g., masked regions in inpainting).

Key Insight: Since both CFG and AG rely on "creating a lower quality denoising result and extrapolating," the most natural way to "degrade quality" for a bridge model is to corrupt the prior available to the model. Since the bridge has not seen perturbed priors, it will produce worse results. This "inferiority" corresponds exactly to "under-utilization of the prior," making the natural extrapolation direction "better utilization of the prior."

Core Idea: Training-freely apply a degradation operator \(\mathcal{H}\) (such as Gaussian noise, blur, or JPEG compression) to \(\bm{x}_T\) and \(\bm{x}_t\) at each step. Use the difference between \(D_{\bm{\theta}}(\bm{x}_t,t,\bm{x}_T)\) and \(D_{\bm{\theta}}(\mathcal{H}(\bm{x}_t),t,\bm{x}_T)\) for guidance extrapolation, and schedule the guidance scale on high/low frequency bands according to the U-shaped SNR.

Method

Overall Architecture

The input consists of a pre-trained bridge model (DDBM / DBIM) and a clean prior \(\bm{x}_T\) (e.g., an image to be translated or restored). During generation, instead of calling a single \(D_{\bm{\theta}}(\bm{x}_t,t,\bm{x}_T)\) to predict \(\bm{x}_0\), the following occurs at each sampling step:

1. A degradation operator \(\mathcal{H}\) corrupts the current noisy latent \(\bm{x}_t\) into a "weak prior" \(\mathcal{H}(\bm{x}_t)\) (\(\bm{x}_T\) is always kept as a clean conditional signal and remains undecayed);
2. Both \(D_{\bm{\theta}}(\bm{x}_t,t,\bm{x}_T)\) and \(D_{\bm{\theta}}(\mathcal{H}(\bm{x}_t),t,\bm{x}_T)\) are called to obtain strong and weak denoising results;
3. The original denoising output is replaced by the extrapolation \(D_{\text{PG}} = D_{\text{weak}} + w_{\text{PG}}(D_{\text{strong}} - D_{\text{weak}})\);
4. FMPG further splits this extrapolation into low/high frequency bands with corresponding weights \(w^{\text{LF}}_{\text{PG}}\) and \(w^{\text{HF}}_{\text{PG}}\);
5. For weak-prior tasks like inpainting, CFG is used for \(t\in[T,t_s)\) to generate coarse structures, then switched to FMPG for \(t\in[t_s,0)\) for detail refinement (CFG-FMPG cascade).

The entire process requires no training and adds no parameters, merely replacing denoising calls during sampling. The NFE is strictly aligned with the baseline (compensating for the extra forward pass per step by using fewer sampling steps).

Key Designs

1. Prior Guidance (PG)—Creating Quality Gaps with Degraded Priors:

   • Function: Transfers the "gap-creation \(\rightarrow\) extrapolation" paradigm of CFG/AG to bridge models, using "degraded prior results" as the source of the gap.
   • Mechanism: A training-free degradation operator \(\mathcal{H}\) (defaulting to additive Gaussian noise \(\bm{\epsilon}\sim\mathcal{N}(\bm{0},\bm{I})\)) is applied to the clean prior and each intermediate latent \(\bm{x}_t\) to obtain \(\mathcal{H}(\bm{x}_t)\). Since the bridge never encountered such degraded priors during pre-training, the result \(D_{\bm{\theta}}(\mathcal{H}(\bm{x}_t),t,\bm{x}_T)\) is inevitably worse than \(D_{\bm{\theta}}(\bm{x}_t,t,\bm{x}_T)\). The extrapolation \(D_{\text{PG}} = D_{\bm{\theta}}(\mathcal{H}(\bm{x}_t),t,\bm{x}_T) + w_{\text{PG}}\,(D_{\bm{\theta}}(\bm{x}_t,t,\bm{x}_T) - D_{\bm{\theta}}(\mathcal{H}(\bm{x}_t),t,\bm{x}_T))\) naturally points towards "fuller prior utilization." The conditional signal \(\bm{x}_T\) remains clean in the weak term to ensure the difference stems only from prior degradation.
   • Design Motivation: Compared to AG, which requires an under-trained network, PG is entirely training-free. Compared to CFG’s "conditional alignment," PG directly addresses the bridge model's core advantage—prior exploitation. Robustness is observed across noise, blur, and JPEG compression.

2. Frequency-modulated PG (FMPG)—Band-split Scheduling per U-shaped SNR:

   • Function: Allows the guidance scale to be "targeted" along the sampling trajectory and frequency dimensions, rather than using a constant \(w_{\text{PG}}\).
   • Mechanism: By tracing the frequency-domain energy distribution of \(\Delta\bm{x}_t \to \Delta\bm{x}_0\), the authors found that because bridge SNR is U-shaped, HF (high frequency) priors are heavily submerged in noise at intermediate timesteps—forcing guidance here amplifies noise. Conversely, LF (low frequency) priors remain readable throughout the trajectory—making intermediate steps ideal for LF enhancement. Thus, PG extrapolation is split: LF is extracted via a low-pass filter \(I^{\text{LF}}\) with an inverted U-shaped \(w^{\text{LF}}_{\text{PG}}\) (amplified in the middle); HF is extracted via \(I^{\text{HF}}\) with a U-shaped \(w^{\text{HF}}_{\text{PG}}\) (suppressed in the middle), formulated as \(D^{\text{LF}}_{\text{FMPG}} = I^{\text{LF}}[D_{\text{weak}}] + w^{\text{LF}}_{\text{PG}}\,(I^{\text{LF}}[D_{\text{strong}}] - I^{\text{LF}}[D_{\text{weak}}])\).
   • Design Motivation: The U-shaped SNR is a geometric feature of the data-to-data paradigm, unique to bridges. FMPG encodes this geometry into the guidance schedule, aligning guidance with bridge generation dynamics. The U/inverted-U shapes are empirical coarse schedules, making FMPG a lightweight training-free plug-in.

3. CFG-FMPG Cascade—Rescuing Weak Prior Tasks:

   • Function: When the prior itself is difficult to use (e.g., a 128x128 center mask in inpainting where no pixel information exists for PG degradation), CFG is utilized to draw the coarse structure before FMPG takes over for detail refinement.
   • Mechanism: The sampling trajectory is divided: early \(t\in[T,t_s)\) uses CFG on class labels \(\bm{l}\) for conditional alignment to fill the mask with semantic structure; then \(t\in[t_s,0)\) switches to FMPG, exploiting the CFG result as a "sufficiently strong prior." Both stages share the same bridge network and trajectory, keeping NFE unchanged.
   • Design Motivation: PG alone fails on inpainting (no difference to create between strong/weak priors), while CFG alone only strengthens semantics without high-frequency detail. CFG and FMPG are complementary in "semantic alignment" and "prior exploitation."

Loss & Training

Entirely training-free. All bridge checkpoints are used as-is (DDBM with the recommended hybrid SDE-ODE sampler, DBIM in pure ODE mode with \(\eta=0.0\)). Hyperparameter tuning involves two steps: selecting a degradation operator \(\mathcal{H}\) from {noise, blur, JPEG, pooling}, then adjusting \(w_{\text{PG}}\) (including FMPG band components).

Key Experimental Results

Main Results

NFE is strictly aligned with the baseline (fewer steps to compensate for the extra forward pass).

Dataset	Metric	DBIM (Baseline)	DBIM+FMPG (Ours)	NFE
Edges→Handbags 64×64	FID ↓	1.74	1.07	20
Edges→Handbags 64×64	FID ↓	0.91	0.78	100
DIODE-Outdoor 256×256	FID ↓	4.99	3.20	20
DIODE-Outdoor 256×256	FID ↓	2.58	2.06	100
DIODE	LPIPS ↓	0.201	0.199	20
Edges→Handbags	MSE ↓	0.005	0.005	20

Also effective on DDBM: DDBM+PG reduces FID on Edges→Handbags at NFE=150 / 300 from 1.30 / 0.65 to 1.23 / 0.59.

Ablation Study

Comparison of PG variants and FMPG on DIODE (baseline is DBIM):

Configuration	NFE=10 FID	NFE=20 FID	NFE=40 FID	Notes
DBIM (No guidance)	7.99	4.99	3.35	Original baseline
ECSI (Parallel work)	6.83	4.12	-	Fast sampler only
DBIM+PG (Blur)	7.33	3.89	2.64	Degradation via blur
DBIM+PG (Noise)	6.25	3.77	2.96	Degradation via noise
DBIM+FMPG (Noise)	5.28	3.20	2.62	Best after freq modulation

Key Findings

• FMPG > PG > Baseline: Splitting constant \(w_{\text{PG}}\) into U-shaped + inverted U-shaped band schedules further reduces FID across all NFEs, proving that the bridge's U-shaped SNR and frequency behavior benefit from a specialized schedule.
• Greater Gains at Lower NFE: On DIODE at NFE=10, FID drops from 7.99 \(\rightarrow\) 5.28 (-34%); at NFE=100 from 2.58 \(\rightarrow\) 2.06 (-20%). FMPG is particularly valuable for fast sampling by "squeezing" out prior information unused in few-step sampling.
• CFG-FMPG is the key to Inpainting: In center-mask inpainting, PG alone creates no difference; however, the CFG-FMPG cascade outperforms both pure CFG and simple hybrids. Qualitative results show simultaneous recovery of semantic layout and high-frequency textures.

Highlights & Insights

• The Third Entry in the "Gap-Creation" Paradigm: CFG creates a "conditional vs. unconditional" gap; AG creates a "well-trained vs. under-trained" gap; PG creates a "clean vs. degraded prior" gap. These are orthogonal, implying multiple guidance types can be stacked; CFG-FMPG is a miniature demonstration.
• Training-free yet Physically Interpretable: The U-shaped HF schedule is not just a trick; it stems from the visualization of \(\Delta\bm{x}_t \to \Delta\bm{x}_0\) energy transfer—high frequencies cannot pass through intermediate steps, so guidance should retreat. This "diagnose then schedule" design pattern can be applied to audio/video bridges.
• Honest NFE-aligned Comparison: Matching total NFE by using fewer steps with extra forward passes avoids "trading 2× compute for performance," ensuring PG/FMPG truly qualifies as a "free lunch."

Limitations & Future Work

• Degradation Operator Requires per-task Search: The optimal choice between noise, blur, or JPEG depends on the dataset; a theoretical understanding of why certain degradations favor specific tasks is missing.
• Manual Frequency Schedule: While the U-shape is derived from SNR observations, the exact peak positions and magnitudes still require tuning. An adaptive schedule might be superior.
• Domain Scope: Only image translation and restoration were verified. Whether FMPG transfers to audio super-resolution or video bridges remains unexamined.

Related Work & Insights

• vs. CFG (Ho & Salimans, 2021): CFG enhances conditional alignment based on condition presence; PG enhances prior exploitation based on prior integrity. They are orthogonal on bridges.
• vs. AG (Karras et al., 2024): AG requires an under-trained network; PG uses training-free degradation during inference, resulting in lower deployment costs and more direct alignment with bridge-specific prior exploitation.
• vs. DDBM / DBIM (Zhou et al., 2024; Zheng et al., 2025): These provide bridge training and fast samplers. Ours serves as a universal enhancement plug-in that leaves their parameters untouched.
• vs. ECSI (Zhang et al., 2025b): ECSI focuses on smarter sampling; PG/FMPG focuses on guidance. Theoretically, they can be combined to further reduce FID at low NFEs.

Rating

• Novelty: ⭐⭐⭐⭐ Porting the "gap-creation" paradigm to bridges and encoding U-shaped SNR/frequency behavior into guidance is original.
• Experimental Thoroughness: ⭐⭐⭐⭐ Covers two backbones and multiple tasks across various NFEs, though migration to audio/video is missing.
• Writing Quality: ⭐⭐⭐⭐ Clear unified perspective on guidance types; effective frequency domain analysis and SNR visualizations.
• Value: ⭐⭐⭐⭐ A truly training-free, NFE-neutral plug-in that provides direct value to image translation/restoration tasks using bridge models.

Related Papers

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• [ICML 2026] Factored Classifier-Free Guidance
• [ICML 2026] Bayesian Tensor Decomposition with Diffusion Model Prior
• [ICML 2026] GUDA: Counterfactual Group-wise Training Data Attribution for Diffusion Models via Unlearning