  Generating photos satisfying multiple constraints find broad utility in the
content creation industry. A key hurdle to accomplishing this task is the need
for paired data consisting of all modalities (i.e., constraints) and their
corresponding output. Moreover, existing methods need retraining using paired
data across all modalities to introduce a new condition. This paper proposes a
solution to this problem based on denoising diffusion probabilistic models
(DDPMs). Our motivation for choosing diffusion models over other generative
models comes from the flexible internal structure of diffusion models. Since
each sampling step in the DDPM follows a Gaussian distribution, we show that
there exists a closed-form solution for generating an image given various
constraints. Our method can unite multiple diffusion models trained on multiple
sub-tasks and conquer the combined task through our proposed sampling strategy.
We also introduce a novel reliability parameter that allows using different
off-the-shelf diffusion models trained across various datasets during sampling
time alone to guide it to the desired outcome satisfying multiple constraints.
We perform experiments on various standard multimodal tasks to demonstrate the
effectiveness of our approach. More details can be found in
https://nithin-gk.github.io/projectpages/Multidiff/index.html
