You will be shown an excerpt from a computer science scientific research paper, followed by a question about the paper. Please answer the question. Do not include any text in your response other than the answer.

Context: In the realm of diffusion models, inversion can be performed naïvely by adding noise to an image and then de-noising it through the network. However, this process tends to change the image content significantly. Choi et al. (2021) improve inversion by conditioning the denoising process on noised low-pass filter data from the target image.(Dhariwal & Nichol, 2021) demonstrate that the DDIM (Song et al., 2020) sampling process can be inverted in a closed-form manner, extracting a latent noise map that will produce a given real image. In DALL-E 2 (Ramesh et al., 2022), they build on this method and demonstrate that it can be used to induce changes in the image, such as cross-image interpolations or semantic editing. The later relies on their use of CLIP-based codes to condition the model, and may not be applicable to other methods. For each prompt, we synthesize 64 samples using 50 DDIM steps, calculate the average CLIP-space embedding of the samples, and compute their cosine similarity with the CLIP-space embedding of the textual prompts, where we omit the placeholder S_{*} (i.e. “A photo of on the moon”). Here, a higher score indicates better editing capability and more faithfulness to the prompt itself. Note that our method does not involve the direct optimization of the CLIP-based objective score and, as such, is not sensitive to the adversarial scoring flaws outlined by Nichol et al. (2021).

Question: What is DDIM? What does closed-form manner mean here?
DDIM Is a sampling process that is described in detail in Song et. al 2020. The authors proposed approach samples images after performing multiple DDIM steps.