[Paper] Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants

Source: arXiv - 2512.10857v1

Overview

A new paper by Modi et al. tackles a long‑standing hurdle in generative modeling: learning to generate clean data when only corrupted observations are available. By treating the corruption process as a black‑box and iteratively refining a transport map, the authors propose a self‑consistent stochastic interpolant (SCSI) that can both invert the corruption and serve as a powerful generative model. This opens the door for high‑quality synthesis in domains where pristine training data are impossible to collect, such as medical imaging, remote sensing, and scientific simulations.

Key Contributions

• Self‑consistent stochastic interpolants (SCSI): An iterative algorithm that learns a transport map between corrupted and clean data using only a corrupted dataset and black‑box access to the forward corruption operator.
• Theoretical convergence guarantees: Under mild regularity assumptions, the iterative updates converge to a fixed point that consistently inverts the corruption channel.
• Computational efficiency: Avoids costly variational inference or explicit likelihood estimation; each iteration requires only sampling from the corruption model and evaluating the current transport map.
• Broad applicability: Works with arbitrary, possibly highly nonlinear forward models (e.g., blur, subsampling, physics‑based simulators) without requiring analytic gradients.
• Empirical superiority: Demonstrates state‑of‑the‑art reconstruction quality on image deblurring, compressive sensing, and scientific inverse problems (e.g., tomography, fluid‑flow field reconstruction).

Methodology

1. Problem setup – Let (x) be the unknown clean data and (y = \mathcal{F}(x) + \epsilon) the observed corrupted measurement, where (\mathcal{F}) is an unknown (or only black‑box) forward operator and (\epsilon) is noise. We have a large collection of (y)’s but no paired ((x, y)).

2. Stochastic interpolants – The authors start from the stochastic interpolant framework, which builds a continuous “bridge” between two distributions by mixing samples with a random time variable (t \in [0,1]).

3. Iterative transport update –

   • Initialize a transport map (T^{(0)}) (e.g., identity).
   • At iteration (k), draw a corrupted sample (y) and generate a synthetic clean sample (\tilde{x}=T^{(k)}(y)).
   • Pass (\tilde{x}) through the black‑box forward model to obtain a synthetic corrupted observation (\tilde{y} = \mathcal{F}(\tilde{x}) + \epsilon).
   • Use the pair ((y, \tilde{y})) to compute a self‑consistency loss that measures how well (T^{(k)}) maps (y) to a clean sample whose forward simulation matches the original (y).
   • Update the transport map via stochastic gradient descent on this loss, yielding (T^{(k+1)}).

4. Self‑consistency principle – The loss forces the map to satisfy ( \mathcal{F}(T(y)) \approx y) in distribution, i.e., the forward model applied to the generated clean sample should reproduce the observed corrupted data.

5. Sampling – After convergence, generating a clean sample is as simple as drawing a corrupted observation (or a prior sample) and applying the learned transport map (T^\star).

Results & Findings

• Speed: Training time was roughly 30 % lower than comparable diffusion‑based variational methods because each iteration only needs forward simulations, not back‑propagation through the forward model.
• Robustness: The method remained stable when the forward operator was highly ill‑conditioned (e.g., severe subsampling) and when noise levels varied across the dataset.
• Ablation: Removing the self‑consistency term caused divergence, confirming its central role in aligning the learned transport with the true inverse.

Practical Implications

• Data‑starved domains: Engineers can now train generative models for high‑fidelity simulations (e.g., climate, materials) using only sensor outputs, bypassing the need for costly ground‑truth labeling.
• Inverse‑problem pipelines: SCSI can be plugged into existing reconstruction workflows as a learned prior, improving image quality in medical CT, MRI, and astronomical imaging without redesigning the physics‑based reconstruction code.
• Rapid prototyping: Because the algorithm only requires black‑box calls to the forward model, developers can experiment with new sensors or simulators (e.g., Lidar, CFD) without deriving analytical gradients.
• Privacy‑preserving synthesis: Organizations that can share only anonymized, corrupted data (e.g., blurred faces, encrypted telemetry) can still generate realistic clean samples for downstream tasks.

Limitations & Future Work

• Assumption of a well‑behaved forward model: The convergence proof relies on Lipschitz continuity and bounded noise; highly chaotic or discontinuous simulators may violate these conditions.
• Scalability to ultra‑high‑resolution data: While more efficient than variational alternatives, training on gigapixel imagery still demands substantial compute and memory for the transport map.
• Black‑box access cost: In some scientific settings, each forward simulation is expensive (e.g., full‑physics PDE solves). Future work could integrate surrogate models or multi‑fidelity strategies to reduce this overhead.
• Extension to conditional generation: The current formulation focuses on unconditional synthesis; adapting SCSI to conditional tasks (e.g., class‑conditional generation) is an open direction.

Overall, the self‑consistent stochastic interpolant framework offers a compelling, theoretically grounded route to generative modeling when clean data are out of reach, promising tangible benefits across a spectrum of engineering and scientific applications.

Authors

• Chirag Modi
• Jiequn Han
• Eric Vanden-Eijnden
• Joan Bruna

Paper Information

• arXiv ID: 2512.10857v1
• Categories: cs.LG, cs.AI, stat.ML
• Published: December 11, 2025
• PDF: Download PDF