# Prompt-Guided Dual Latent Steering for Inversion Problems

arXiv: https://arxiv.org/abs/2509.18619 · HTML: https://mlsanity.com/paper/2509.18619/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 30)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translation](https://mlsanity.com/paper/2211.12572/) (2022)
- [DiffEdit: Diffusion-based semantic image editing with mask guidance](https://mlsanity.com/paper/2210.11427/) (2022)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations](https://mlsanity.com/paper/2410.10792/) (2024)
- [Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models](https://mlsanity.com/paper/2307.00619/) (2023)
- [Pretrained Language Models for Text Generation: A Survey](https://mlsanity.com/paper/2201.05273/) (2022)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [RB-Modulation: Training-Free Personalization of Diffusion Models using Stochastic Optimal Control](https://mlsanity.com/paper/2405.17401/) (2024)
- [Diff-Restorer: Unleashing Visual Prompts for Diffusion-based Universal Image Restoration](https://mlsanity.com/paper/2407.03636/) (2024)
- [SEAL: Semantic Attention Learning for Long Video Representation](https://mlsanity.com/paper/2412.01798/) (2024)

## Built on by (most cited first, 5 of 5)

- [ConeSep: Cone-based Robust Noise-Unlearning Compositional Network for Composed Image Retrieval](https://mlsanity.com/paper/2604.20358/) (2026)
- [TEMA: Anchor the Image, Follow the Text for Multi-Modification Composed Image Retrieval](https://mlsanity.com/paper/2604.21806/) (2026)
- [COMBINER: Composed Image Retrieval Guided by Attribute-based Neighbor Relations](https://mlsanity.com/paper/2606.04604/) (2026)
- [IMAGINE: Adaptive Schema-Imagery Enhanced Composition for Composed Video Retrieval](https://mlsanity.com/paper/2606.08144/) (2026)
- [CARE: Training-Free Controllable Restoration for Medical Images via Dual-Latent Steering](https://mlsanity.com/paper/2603.25026/) (2026)

## Abstract (arXiv)

Inverting corrupted images into the latent space of diffusion models is challenging. Current methods, which encode an image into a single latent vector, struggle to balance structural fidelity with semantic accuracy, leading to reconstructions with semantic drift, such as blurred details or incorrect attributes. To overcome this, we introduce Prompt-Guided Dual Latent Steering (PDLS), a novel, training-free framework built upon Rectified Flow models for their stable inversion paths. PDLS decomposes the inversion process into two complementary streams: a structural path to preserve source integrity and a semantic path guided by a prompt. We formulate this dual guidance as an optimal control problem and derive a closed-form solution via a Linear Quadratic Regulator (LQR). This controller dynamically steers the generative trajectory at each step, preventing semantic drift while ensuring the preservation of fine detail without costly, per-image optimization. Extensive experiments on FFHQ-1K and ImageNet-1K under various inversion tasks, including Gaussian deblurring, motion deblurring, super-resolution and freeform inpainting, demonstrate that PDLS produces reconstructions that are both more faithful to the original image and better aligned with the semantic information than single-latent baselines.