Diffusion models have quickly become the state-of-the-art for generation tasks across many different data modalities. An important ability of diffusion models is the ability to encode samples from the data distribution back into the sampling prior distribution. This is useful for performing alterations to real data samples along with guided generation via the continuous adjoint equations. We propose an algebraically reversible solver for diffusion SDEs that can exactly invert real data samples into the prior distribution. Diffusion models have quickly become the state-of-the-art in many different modalities in generation, e.g., audio (Liu et al., 2023), images (Rombach et al., 2022), video (Blattmann et al., 2023), protein generation (Skreta et al., 2024), & c.

Training large language models (LLMs) requires a substantial investment of time and money. To get a good return on investment, the developers spend considerable effort ensuring that the model never produces harmful and offensive outputs. However, bad-faith actors may still try to slander the reputation of an LLM by publicly reporting a forged output. In this paper, we show that defending against such slander attacks requires reconstructing the input of the forged output or proving that it does not exist. To do so, we propose and evaluate a search based approach for targeted adversarial attacks for LLMs. Our experiments show that we are rarely able to reconstruct the exact input of an arbitrary output, thus demonstrating that LLMs are still vulnerable to slander attacks.

Diffusion probabilistic models (DPMs) are a key component in modern generative models. DPM-solvers have achieved reduced latency and enhanced quality significantly, but have posed challenges to find the exact inverse (i.e., finding the initial noise from the given image). Here we investigate the exact inversions for DPM-solvers and propose algorithms to perform them when samples are generated by the first-order as well as higher-order DPM-solvers. For each explicit denoising step in DPM-solvers, we formulated the inversions using implicit methods such as gradient descent or forward step method to ensure the robustness to large classifier-free guidance unlike the prior approach using fixed-point iteration. Experimental results demonstrated that our proposed exact inversion methods significantly reduced the error of both image and noise reconstructions, greatly enhanced the ability to distinguish invisible watermarks and well prevented unintended background changes consistently during image editing. Project page: \url{https://smhongok.github.io/inv-dpm.html}.