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Diffusion Bridge Variational Inference for Deep Gaussian Processes

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Deep Gaussian ProcessesDiffusion BridgeVariational Inference
Abstract:

Deep Gaussian processes (DGPs) enable expressive hierarchical Bayesian modeling but pose substantial challenges for posterior inference, especially over inducing variables. Denoising diffusion variational inference (DDVI) addresses this by modeling the posterior as a time-reversed diffusion from a simple Gaussian prior. However, DDVI’s fixed unconditional starting distribution remains far from the complex true posterior, resulting in inefficient inference trajectories and slow convergence. In this work, we propose Diffusion Bridge Variational Inference (DBVI), a principled extension of DDVI that initiates the reverse diffusion from a learnable, data-dependent initial distribution. This initialization is parameterized via an amortized neural network and progressively adapted using gradients from the ELBO objective, reducing the posterior gap and improving sample efficiency. To enable scalable amortization, we design the network to operate on the inducing inputs Z(l)\mathbf{Z}^{(l)}, which serve as structured, low-dimensional summaries of the dataset and naturally align with the inducing variables' shape. DBVI retains the mathematical elegance of DDVI—including Girsanov-based ELBOs and reverse-time SDEs—while reinterpreting the prior via a Doob-bridged diffusion process. We derive a tractable training objective under this formulation and implement DBVI for scalable inference in large-scale DGPs. Across regression, classification, and image reconstruction tasks, DBVI consistently outperforms DDVI and other variational baselines in predictive accuracy, convergence speed, and posterior quality.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes Diffusion Bridge Variational Inference (DBVI) for posterior inference in deep Gaussian processes, introducing a learnable data-dependent initial distribution for reverse diffusion. According to the taxonomy, this work resides in the 'Bridge-Conditioned Diffusion Variational Inference' leaf under 'Diffusion-Based Variational Inference for Deep Gaussian Processes'. Notably, this leaf contains only the original paper itself (no sibling papers), suggesting this specific combination of bridge conditioning and learnable initialization represents a relatively unexplored direction within the broader diffusion-based inference landscape for deep GPs.

The taxonomy reveals three main branches leveraging diffusion models: variational inference for deep GPs, meta-learning function distributions, and inverse problem posterior sampling. The original work's sibling leaf 'Fixed-Prior Diffusion Variational Inference' contains one paper (DDVI), representing the direct baseline approach with fixed Gaussian priors. Neighboring branches address related but distinct problems—meta-learning over function spaces and denoising tasks—indicating the paper operates within a specialized niche focused on hierarchical Bayesian modeling rather than broader diffusion applications. The taxonomy's scope notes explicitly distinguish bridge-conditioned approaches from fixed-prior methods, positioning DBVI as an extension rather than a departure from existing diffusion-based GP inference.

Among 20 candidates examined, the contribution-level analysis reveals mixed novelty signals. The core DBVI method itself was not refuted by any candidates (0 examined, 0 refutable), suggesting limited direct prior work on this specific formulation. However, the bridge-based reinterpretation using Doob's h-transform shows substantial overlap: 10 candidates examined, 7 refutable, indicating this theoretical component builds on established diffusion bridge theory. The structured amortization strategy using inducing locations examined 10 candidates with 0 refutable, suggesting this architectural choice may be more novel within the limited search scope, though 10 non-refutable/unclear candidates indicate related amortization ideas exist in adjacent contexts.

Based on the limited search scope of 20 semantically similar candidates, DBVI appears to occupy a sparse research direction combining bridge conditioning with learnable initialization for deep GP inference. The theoretical bridge formulation draws heavily on existing diffusion theory, while the amortization strategy and overall method integration show fewer direct precedents among examined candidates. The analysis does not cover exhaustive literature review or broader variational inference methods outside the diffusion framework, leaving open questions about connections to non-diffusion-based approaches for deep GP posteriors.

Taxonomy

Core-task Taxonomy Papers
3
3
Claimed Contributions
20
Contribution Candidate Papers Compared
7
Refutable Paper

Research Landscape Overview

Core task: Posterior inference for deep Gaussian processes using diffusion bridges. The field structure suggested by the taxonomy reveals three main branches that leverage diffusion models in distinct ways. The first branch, Diffusion-Based Variational Inference for Deep Gaussian Processes, focuses on using diffusion processes to approximate complex posterior distributions in deep GP models, often employing bridge-conditioned or inducing-point strategies to manage computational challenges. The second branch, Diffusion Models for Meta-Learning Function Distributions, applies diffusion frameworks to learn distributions over functions in meta-learning contexts, enabling flexible priors and adaptation across tasks. The third branch, Diffusion-Based Posterior Sampling for Inverse Problems, targets inverse problem settings where diffusion models guide sampling from posteriors conditioned on observations. These branches share the common theme of exploiting diffusion processes for probabilistic inference, yet differ in their problem settings and the role diffusion plays—whether as a variational tool, a meta-learning prior, or a sampling mechanism. A particularly active line of work within the first branch explores how to scale diffusion-based variational inference to deep GPs while maintaining tractability. Diffusion Bridge Variational[0] sits squarely in this area, emphasizing bridge-conditioned diffusion to handle the hierarchical structure of deep GPs. This contrasts with approaches like Sparse Inducing Diffusion[1], which leverages inducing points to reduce computational burden, and Divide Conquer Posterior[2], which partitions the inference problem for scalability. Meanwhile, Neural Diffusion Processes[3] operates in the meta-learning branch, learning function distributions rather than focusing on deep GP posteriors. The original work's emphasis on bridge conditioning distinguishes it from these neighbors by directly modeling transitions between latent layers, offering a principled way to capture dependencies in deep hierarchies without relying solely on sparsity or partitioning strategies.

Claimed Contributions

Diffusion Bridge Variational Inference (DBVI) method

The authors introduce DBVI, which extends denoising diffusion variational inference by using a learnable, data-dependent initial distribution instead of a fixed Gaussian prior. This reduces the inference gap and improves posterior approximation efficiency in deep Gaussian processes.

0 retrieved papers
Bridge-based reinterpretation using Doob's h-transform

The authors develop a theoretical framework that incorporates Doob's h-transform to reinterpret DDVI as a bridge process. This preserves the mathematical foundations of reverse-time SDEs and ELBO construction while enabling observation-conditioned diffusion bridges.

10 retrieved papers
Can Refute
Structured amortization strategy using inducing locations

The authors design an amortization approach that uses inducing inputs as structured, low-dimensional summaries for the amortizer network. This enables scalable batch-wise inference while avoiding dimensional mismatches and overfitting issues associated with direct conditioning on raw inputs.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Diffusion Bridge Variational Inference (DBVI) method

The authors introduce DBVI, which extends denoising diffusion variational inference by using a learnable, data-dependent initial distribution instead of a fixed Gaussian prior. This reduces the inference gap and improves posterior approximation efficiency in deep Gaussian processes.

Contribution

Bridge-based reinterpretation using Doob's h-transform

The authors develop a theoretical framework that incorporates Doob's h-transform to reinterpret DDVI as a bridge process. This preserves the mathematical foundations of reverse-time SDEs and ELBO construction while enabling observation-conditioned diffusion bridges.

Contribution

Structured amortization strategy using inducing locations

The authors design an amortization approach that uses inducing inputs as structured, low-dimensional summaries for the amortizer network. This enables scalable batch-wise inference while avoiding dimensional mismatches and overfitting issues associated with direct conditioning on raw inputs.

Table of Contents