Diffusion probabilistic models generate images by running two linked processes: a forward process that gradually buries an image in Gaussian noise, and a reverse process trained to predict that noise and denoise pure randomness back into a clean image. The original DDPM formulation reached an Inception score of 9.46 and an FID of 3.17 on CIFAR10, and the same principle now powers production tools like Stable Diffusion.
What Is a Diffusion Probabilistic Model?
The original Denoising Diffusion Probabilistic Models (DDPM) paper presents diffusion probabilistic models as a class of latent variable models, inspired by nonequilibrium thermodynamics, that produce high-quality image synthesis resultsCITE:E1. That framing — a physics-inspired latent variable model rather than a single fixed generation step — is the foundation the rest of the technique builds on: an image is not produced in one shot, but recovered gradually across many steps.
How Does the Forward Process Gradually Corrupt Images With Noise?
The forward process gradually destroys an image by adding Gaussian noise at each timestep and then rescaling the result to keep its size constantCITE:E7CITE:E3. NVIDIA frames this as the "easy direction" to start from: begin by considering how to destroy an image by gradually adding noise onto itCITE:E7. At each timestep t, a small amount of Gaussian noise is added to the previous image, and the image is then rescaled to maintain a constant image sizeCITE:E3. Repeated enough times, this sequence turns a structured image into what is effectively pure Gaussian noise.
How Does the Model Learn to Predict and Remove Noise in Reverse?
The reverse process trains the model to undo each noising step, denoising pure Gaussian noise into a clean imageCITE:E4. In learning to perform the reverse of the noising steps of the forward process, the model is essentially learning to denoise pure Gaussian noise into a clean imageCITE:E4. Critically, at each image step the model is trained to predict the entire noise that was added, rather than the specific amount of noise to be removed at that particular stepCITE:E5. That distinction — predicting the full noise rather than a single step's residual — is the specific mechanism that lets the reverse process reconstruct an image from randomness.
What Results and Applications Have Diffusion Models Achieved?
DDPM reached an Inception score of 9.46 and a then-state-of-the-art FID score of 3.17 on the unconditional CIFAR10 datasetCITE:E2. On the same unconditional CIFAR10 benchmark, the paper reports both figures together as evidence of image qualityCITE:E2. The same denoising principle extends beyond benchmarks into applied products: Stable Diffusion is a generative AI model that produces unique photorealistic images from text and image promptsCITE:E6.
Taken together, the evidence traces one mechanism end to end. The forward process buries an image in Gaussian noise step by stepCITE:E7CITE:E3, and the reverse process is trained specifically to predict the entire noise added at each step rather than a stepwise residual, so it can denoise pure Gaussian noise back into a clean imageCITE:E4CITE:E5. That is the same latent-variable formulation the original DDPM paper describesCITE:E1, backed by concrete CIFAR10 scores of Inception 9.46 and FID 3.17CITE:E2, and it is the principle underlying Stable Diffusion's text-and-image-prompt image generationCITE:E6.