A Visual Guide to How Diffusion Models Work

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A Visual Guide to How Diffusion Models Work

This article is aimed at those who want to understand exactly how Diffusion Models work, with no prior knowledge expected. I’ve tried to use illustrations wherever possible to provide visual intuitions on each part of these models. I’ve kept mathematical notation and equations to a minimum, and where they are necessary I’ve tried to define […]

Intro

I’ve framed this article around three main questions:

What exactly is it that diffusion models learn?
How and why do diffusion models work?
Once you’ve trained a model, how do you get useful stuff out of it?

The examples will be based on the glyffuser, a minimal text-to-image diffusion model that I previously implemented and wrote about. The architecture of this model is a standard text-to-image denoising diffusion model without any bells or whistles. It was trained to generate pictures of new “Chinese” glyphs from English definitions. Have a look at the picture below — even if you’re not familiar with Chinese writing, I hope you’ll agree that the generated glyphs look pretty similar to the real ones!

Random examples of glyffuser training data (left) and generated data (right).

What exactly is it that diffusion models learn?

Generative Ai models are often said to take a big pile of data and “learn” it. For text-to-image diffusion models, the data takes the form of pairs of images and descriptive text. But what exactly is it that we want the model to learn? First, let’s forget about the text for a moment and concentrate on what we are trying to generate: the images.

Probability distributions

Broadly, we can say that we want a generative AI model to learn the underlying probability distribution of the data. What does this mean? Consider the one-dimensional normal (Gaussian) distribution below, commonly written 𝒩(μ,σ²) and parameterized with mean μ = 0 and variance σ² = 1. The black curve below shows the probability density function. We can sample from it: drawing values such that over a large number of samples, the set of values reflects the underlying distribution. These days, we can simply write something like x = random.gauss(0, 1) in Python to sample from the standard normal distribution, although the computational sampling process itself is non-trivial!

Values sampled from an underlying distribution (here, the standard normal 𝒩(0,1)) can then be used to estimate the parameters of that distribution.

We could think of a set of numbers sampled from the above normal distribution as a simple dataset, like that shown as the orange histogram above. In this particular case, we can calculate the parameters of the underlying distribution using maximum likelihood estimation, i.e. by working out the mean and variance. The normal distribution estimated from the samples is shown by the dotted line above. To take some liberties with terminology, you might consider this as a simple example of “learning” an underlying probability distribution. We can also say that here we explicitly learnt the distribution, in contrast with the implicit methods that diffusion models use.

Conceptually, this is all that generative AI is doing — learning a distribution, then sampling from that distribution!

Data representations

What, then, does the underlying probability distribution of a more complex dataset look like, such as that of the image dataset we want to use to train our diffusion model?

First, we need to know what the representation of the data is. Generally, a machine learning (ML) model requires data inputs with a consistent representation, i.e. format. For the example above, it was simply numbers (scalars). For images, this representation is commonly a fixed-length vector.

The image dataset used for the glyffuser model is ~21,000 pictures of Chinese glyphs. The images are all the same size, 128 × 128 = 16384 pixels, and greyscale (single-channel color). Thus an obvious choice for the representation is a vector x of length 16384, where each element corresponds to the color of one pixel: x = (x₁,x₂,…,x₁₆₃₈₄). We can call the domain of all possible images for our dataset “pixel space”.

An example glyph with pixel values labelled (downsampled to 32 × 32 pixels for readability).

Dataset visualization

We make the assumption that our individual data samples, x, are actually sampled from an underlying probability distribution, q(x), in pixel space, much as the samples from our first example were sampled from an underlying normal distribution in 1-dimensional space. Note: the notation x ∼ q(x) is commonly used to mean: “the random variable x sampled from the probability distribution q(x).”

This distribution is clearly much more complex than a Gaussian and cannot be easily parameterized — we need to learn it with a ML model, which we’ll discuss later. First, let’s try to visualize the distribution to gain a better intution.

As humans find it difficult to see in more than 3 dimensions, we need to reduce the dimensionality of our data. A small digression on why this works: the manifold hypothesis posits that natural datasets lie on lower dimensional manifolds embedded in a higher dimensional space — think of a line embedded in a 2-D plane, or a plane embedded in 3-D space. We can use a dimensionality reduction technique such as UMAP to project our dataset from 16384 to 2 dimensions. The 2-D projection retains a lot of structure, consistent with the idea that our data lie on a lower dimensional manifold embedded in pixel space. In our UMAP, we see two large clusters corresponding to characters in which the components are arranged either horizontally (e.g. 明) or vertically (e.g. 草). An interactive version of the plot below with popups on each datapoint is linked here.

Click here for an interactive version of this plot.

Let’s now use this low-dimensional UMAP dataset as a visual shorthand for our high-dimensional dataset. Remember, we assume that these individual points have been sampled from a continuous underlying probability distribution q(x). To get a sense of what this distribution might look like, we can apply a KDE (kernel density estimation) over the UMAP dataset. (Note: this is just an approximation for visualization purposes.)

This gives a sense of what q(x) should look like: clusters of glyphs correspond to high-probability regions of the distribution. The true q(x) lies in 16384 dimensions — this is the distribution we want to learn with our diffusion model.

We showed that for a simple distribution such as the 1-D Gaussian, we could calculate the parameters (mean and variance) from our data. However, for complex distributions such as images, we need to call on ML methods. Moreover, what we will find is that for diffusion models in practice, rather than parameterizing the distribution directly, they learn it implicitly through the process of learning how to transform noise into data over many steps.

Takeaway

The aim of generative AI such as diffusion models is to learn the complex probability distributions underlying their training data and then sample from these distributions.

How and why do diffusion models work?

Diffusion models have recently come into the spotlight as a particularly effective method for learning these probability distributions. They generate convincing images by starting from pure noise and gradually refining it. To whet your interest, have a look at the animation below that shows the denoising process generating 16 samples.

In this section we’ll only talk about the mechanics of how these models work but if you’re interested in how they arose from the broader context of generative models, have a look at the further reading section below.

What is “noise”?

Let’s first precisely define noise, since the term is thrown around a lot in the context of diffusion. In particular, we are talking about Gaussian noise: consider the samples we talked about in the section about probability distributions. You could think of each sample as an image of a single pixel of noise. An image that is “pure Gaussian noise”, then, is one in which each pixel value is sampled from an independent standard Gaussian distribution, 𝒩(0,1). For a pure noise image in the domain of our glyph dataset, this would be noise drawn from 16384 separate Gaussian distributions. You can see this in the previous animation. One thing to keep in mind is that we can choose the means of these noise distributions, i.e. center them, on specific values — the pixel values of an image, for instance.

For convenience, you’ll often find the noise distributions for image datasets written as a single multivariate distribution 𝒩(0,I) where I is the identity matrix, a covariance matrix with all diagonal entries equal to 1 and zeroes elsewhere. This is simply a compact notation for a set of multiple independent Gaussians — i.e. there are no correlations between the noise on different pixels. In the basic implementations of diffusion models, only uncorrelated (a.k.a. “isotropic”) noise is used. This article contains an excellent interactive introduction on multivariate Gaussians.

Diffusion process overview

Below is an adaptation of the somewhat-famous diagram from Ho et al.’s seminal paper “Denoising Diffusion Probabilistic Models” which gives an overview of the whole diffusion process:

Diagram of the diffusion process adapted from Ho *et al*. 2020. The glyph 锂, meaning “lithium”, is used as a representative sample from the dataset.

I found that there was a lot to unpack in this diagram and simply understanding what each component meant was very helpful, so let’s go through it and define everything step by step.

We previously used x ∼ q(x) to refer to our data. Here, we’ve added a subscript, xₜ, to denote timestep t indicating how many steps of “noising” have taken place. We refer to the samples noised a given timestep as x ∼ q(xₜ). x₀ is clean data and xₜ (t = T) ∼ 𝒩(0,1) is pure noise.

We define a forward diffusion process whereby we corrupt samples with noise. This process is described by the distribution q(xₜ|xₜ₋₁). If we could access the hypothetical reverse process q(xₜ₋₁|xₜ), we could generate samples from noise. As we cannot access it directly because we would need to know x₀, we use ML to learn the parameters, θ, of a model of this process, 𝑝θ(𝑥ₜ₋₁∣𝑥ₜ). (That should be p subscript θ but medium cannot render it.)

In the following sections we go into detail on how the forward and reverse diffusion processes work.

Forward diffusion, or “noising”

Used as a verb, “noising” an image refers to applying a transformation that moves it towards pure noise by scaling down its pixel values toward 0 while adding proportional Gaussian noise. Mathematically, this transformation is a multivariate Gaussian distribution centered on the pixel values of the preceding image.

In the forward diffusion process, this noising distribution is written as q(xₜ|xₜ₋₁) where the vertical bar symbol “|” is read as “given” or “conditional on”, to indicate the pixel means are passed forward from q(xₜ₋₁) At t = T where T is a large number (commonly 1000) we aim to end up with images of pure noise (which, somewhat confusingly, is also a Gaussian distribution, as discussed previously).

The marginal distributions q(xₜ) represent the distributions that have accumulated the effects of all the previous noising steps (marginalization refers to integration over all possible conditions, which recovers the unconditioned distribution).

Since the conditional distributions are Gaussian, what about their variances? They are determined by a variance schedule that maps timesteps to variance values. Initially, an empirically determined schedule of linearly increasing values from 0.0001 to 0.02 over 1000 steps was presented in Ho et al. Later research by Nichol & Dhariwal suggested an improved cosine schedule. They state that a schedule is most effective when the rate of information destruction through noising is relatively even per step throughout the whole noising process.

Forward diffusion intuition

As we encounter Gaussian distributions both as pure noise q(xₜ, t = T) and as the noising distribution q(xₜ|xₜ₋₁), I’ll try to draw the distinction by giving a visual intuition of the distribution for a single noising step, q(x₁∣x₀), for some arbitrary, structured 2-dimensional data:

Each noising step q(xₜ|xₜ₋₁) is a Gaussian distribution conditioned on the previous step.

The distribution q(x₁∣x₀) is Gaussian, centered around each point in x₀, shown in blue. Several example points x₀⁽ⁱ⁾ are picked to illustrate this, with q(x₁∣x₀ = x₀⁽ⁱ⁾) shown in orange.

In practice, the main usage of these distributions is to generate specific instances of noised samples for training (discussed further below). We can calculate the parameters of the noising distributions at any timestep t directly from the variance schedule, as the chain of Gaussians is itself also Gaussian. This is very convenient, as we don’t need to perform noising sequentially—for any given starting data x₀⁽ⁱ⁾, we can calculate the noised sample xₜ⁽ⁱ⁾ by sampling from q(xₜ∣x₀ = x₀⁽ⁱ⁾) directly.

Forward diffusion visualization

Let’s now return to our glyph dataset (once again using the UMAP visualization as a visual shorthand). The top row of the figure below shows our dataset sampled from distributions noised to various timesteps: xₜ ∼ q(xₜ). As we increase the number of noising steps, you can see that the dataset begins to resemble pure Gaussian noise. The bottom row visualizes the underlying probability distribution q(xₜ).

The dataset xₜ (above) sampled from its probability distribution q(xₜ) (below) at different noising timesteps.

Reverse diffusion overview

It follows that if we knew the reverse distributions q(xₜ₋₁∣xₜ), we could repeatedly subtract a small amount of noise, starting from a pure noise sample xₜ at t = T to arrive at a data sample x₀ ∼ q(x₀). In practice, however, we cannot access these distributions without knowing x₀ beforehand. Intuitively, it’s easy to make a known image much noisier, but given a very noisy image, it’s much harder to guess what the original image was.

So what are we to do? Since we have a large amount of data, we can train an ML model to accurately guess the original image that any given noisy image came from. Specifically, we learn the parameters θ of an ML model that approximates the reverse noising distributions, pθ(xₜ₋₁ ∣ xₜ) for t = 0, …, T. In practice, this is embodied in a single noise prediction model trained over many different samples and timesteps. This allows it to denoise any given input, as shown in the figure below.

The ML model predicts added noise at any given timestep t.

Next, let’s go over how this noise prediction model is implemented and trained in practice.

How the model is implemented

First, we define the ML model — generally a deep neural network of some sort — that will act as our noise prediction model. This is what does the heavy lifting! In practice, any ML model that inputs and outputs data of the correct size can be used; the U-net, an architecture particularly suited to learning images, is what we use here and frequently chosen in practice. More recent models also use vision transformers.

We use the U-net architecture (Ronneberger *et al*. 2015) for our ML noise prediction model. We train the model by minimizing the difference between predicted and actual noise.

Then we run the training loop depicted in the figure above:

We take a random image from our dataset and noise it to a random timestep tt. (In practice, we speed things up by doing many examples in parallel!)
We feed the noised image into the ML model and train it to predict the (known to us) noise in the image. We also perform timestep conditioning by feeding the model a timestep embedding, a high-dimensional unique representation of the timestep, so that the model can distinguish between timesteps. This can be a vector the same size as our image directly added to the input (see here for a discussion of how this is implemented).
The model “learns” by minimizing the value of a loss function, some measure of the difference between the predicted and actual noise. The mean square error (the mean of the squares of the pixel-wise difference between the predicted and actual noise) is used in our case.
Repeat until the model is well trained.

Note: A neural network is essentially a function with a huge number of parameters (on the order of 10⁶ for the glyffuser). Neural network ML models are trained by iteratively updating their parameters using backpropagation to minimize a given loss function over many training data examples. This is an excellent introduction. These parameters effectively store the network’s “knowledge”.

A noise prediction model trained in this way eventually sees many different combinations of timesteps and data examples. The glyffuser, for example, was trained over 100 epochs (runs through the whole data set), so it saw around 2 million data samples. Through this process, the model implicity learns the reverse diffusion distributions over the entire dataset at all different timesteps. This allows the model to sample the underlying distribution q(x₀) by stepwise denoising starting from pure noise. Put another way, given an image noised to any given level, the model can predict how to reduce the noise based on its guess of what the original image. By doing this repeatedly, updating its guess of the original image each time, the model can transform any noise to a sample that lies in a high-probability region of the underlying data distribution.

Reverse diffusion in practice

We can now revisit this video of the glyffuser denoising process. Recall a large number of steps from sample to noise e.g. T = 1000 is used during training to make the noise-to-sample trajectory very easy for the model to learn, as changes between steps will be small. Does that mean we need to run 1000 denoising steps every time we want to generate a sample?

Luckily, this is not the case. Essentially, we can run the single-step noise prediction but then rescale it to any given step, although it might not be very good if the gap is too large! This allows us to approximate the full sampling trajectory with fewer steps. The video above uses 120 steps, for instance (most implementations will allow the user to set the number of sampling steps).

Recall that predicting the noise at a given step is equivalent to predicting the original image x₀, and that we can access the equation for any noised image deterministically using only the variance schedule and x₀. Thus, we can calculate xₜ₋ₖ based on any denoising step. The closer the steps are, the better the approximation will be.

Too few steps, however, and the results become worse as the steps become too large for the model to effectively approximate the denoising trajectory. If we only use 5 sampling steps, for example, the sampled characters don’t look very convincing at all:

There is then a whole literature on more advanced sampling methods beyond what we’ve discussed so far, allowing effective sampling with much fewer steps. These often reframe the sampling as a differential equation to be solved deterministically, giving an eerie quality to the sampling videos — I’ve included one at the end if you’re interested. In production-level models, these are usually preferred over the simple method discussed here, but the basic principle of deducing the noise-to-sample trajectory is the same. A full discussion is beyond the scope of this article but see e.g. this paper and its corresponding implementation in the Hugging Face diffusers library for more information.

Alternative intuition from score function

To me, it was still not 100% clear why training the model on noise prediction generalises so well. I found that an alternative interpretation of diffusion models known as “score-based modeling” filled some of the gaps in intuition (for more information, refer to Yang Song’s definitive article on the topic.)

The dataset xₜ sampled from its probability distribution q(xₜ) at different noising timesteps; below, we add the score function ∇ₓ log q(xₜ).

I try to give a visual intuition in the bottom row of the figure above: essentially, learning the noise in our diffusion model is equivalent (to a constant factor) to learning the score function, which is the gradient of the log of the probability distribution: ∇ₓ log q(x). As a gradient, the score function represents a vector field with vectors pointing towards the regions of highest probability density. Subtracting the noise at each step is then equivalent to moving following the directions in this vector field towards regions of high probability density.

As long as there is some signal, the score function effectively guides sampling, but in regions of low probability it tends towards zero as there is little to no gradient to follow. Using many steps to cover different noise levels allows us to avoid this, as we smear out the gradient field at high noise levels, allowing sampling to converge even if we start from low probability density regions of the distribution. The figure shows that as the noise level is increased, more of the domain is covered by the score function vector field.

Summary

The aim of diffusion models is learn the underlying probability distribution of a dataset and then be able to sample from it. This requires forward and reverse diffusion (noising) processes.
The forward noising process takes samples from our dataset and gradually adds Gaussian noise (pushes them off the data manifold). This forward process is computationally efficient because any level of noise can be added in closed form a single step.
The reverse noising process is challenging because we need to predict how to remove the noise at each step without knowing the original data point in advance. We train a ML model to do this by giving it many examples of data noised at different timesteps.
Using very small steps in the forward noising process makes it easier for the model to learn to reverse these steps, as the changes are small.
By applying the reverse noising process iteratively, the model refines noisy samples step by step, eventually producing a realistic data point (one that lies on the data manifold).

Takeaway

Diffusion models are a powerful framework for learning complex data distributions. The distributions are learnt implicitly by modelling a sequential denoising process. This process can then be used to generate samples similar to those in the training distribution.

Once you’ve trained a model, how do you get useful stuff out of it?

Earlier uses of generative AI such as “This Person Does Not Exist” (ca. 2019) made waves simply because it was the first time most people had seen AI-generated photorealistic human faces. A generative adversarial network or “GAN” was used in that case, but the principle remains the same: the model implicitly learnt a underlying data distribution — in that case, human faces — then sampled from it. So far, our glyffuser model does a similar thing: it samples randomly from the distribution of Chinese glyphs.

The question then arises: can we do something more useful than just sample randomly? You’ve likely already encountered text-to-image models such as Dall-E. They are able to incorporate extra meaning from text prompts into the diffusion process — this in known as conditioning. Likewise, diffusion models for scientific scientific applications like protein (e.g. Chroma, RFdiffusion, AlphaFold3) or inorganic crystal structure generation (e.g. MatterGen) become much more useful if can be conditioned to generate samples with desirable properties such as a specific symmetry, bulk modulus, or band gap.

Conditional distributions

We can consider conditioning as a way to guide the diffusion sampling process towards particular regions of our probability distribution. We mentioned conditional distributions in the context of forward diffusion. Below we show how conditioning can be thought of as reshaping a base distribution.

A simple example of a joint probability distribution p(x, y), shown as a contour map, along with its two marginal 1-D probability distributions, p(x) and p(y). The highest points of p(x, y) are at (x₁, y₁) and (x₂, y₂). The conditional distributions p(x∣y = y₁) and p(x∣y = y₂) are shown overlaid on the main plot.

Consider the figure above. Think of p(x) as a distribution we want to sample from (i.e., the images) and p(y) as conditioning information (i.e., the text dataset). These are the marginal distributions of a joint distribution p(x, y). Integrating p(x, y) over y recovers p(x), and vice versa.

Sampling from p(x), we are equally likely to get x₁ or x₂. However, we can condition on p(y = y₁) to obtain p(x∣y = y₁). You can think of this as taking a slice through p(x, y) at a given value of y. In this conditioned distribution, we are much more likely to sample at x₁ than x₂.

In practice, in order to condition on a text dataset, we need to convert the text into a numerical form. We can do this using large language model (LLM) embeddings that can be injected into the noise prediction model during training.

Embedding text with an LLM

In the glyffuser, our conditioning information is in the form of English text definitions. We have two requirements: 1) ML models prefer fixed-length vectors as input. 2) The numerical representation of our text must understand context — if we have the words “lithium” and “element” nearby, the meaning of “element” should be understood as “chemical element” rather than “heating element”. Both of these requirements can be met by using a pre-trained LLM.

The diagram below shows how an LLM converts text into fixed-length vectors. The text is first tokenized (LLMs break text into tokens, small chunks of characters, as their basic unit of interaction). Each token is converted into a base embedding, which is a fixed-length vector of the size of the LLM input. These vectors are then passed through the pre-trained LLM (here we use the encoder portion of Google’s T5 model), where they are imbued with additional contextual meaning. We end up with a array of n vectors of the same length d, i.e. a (n, d) sized tensor.

We can convert text to a numerical embedding imbued with contextual meaning using a pre-trained LLM.

Note: in some models, notably Dall-E, additional image-text alignment is performed using contrastive pretraining. Imagen seems to show that we can get away without doing this.

Training the diffusion model with text conditioning

The exact method that this embedding vector is injected into the model can vary. In Google’s Imagen model, for example, the embedding tensor is pooled (combined into a single vector in the embedding dimension) and added into the data as it passes through the noise prediction model; it is also included in a different way using cross-attention (a method of learning contextual information between sequences of tokens, most famously used in the transformer models that form the basis of LLMs like ChatGPT).

Conditioning information can be added *via* multiple different methods but the training loss remains the same.

In the glyffuser, we only use cross-attention to introduce this conditioning information. While a significant architectural change is required to introduce this additional information into the model, the loss function for our noise prediction model remains exactly the same.

Testing the conditioned diffusion model

Let’s do a simple test of the fully trained conditioned diffusion model. In the figure below, we try to denoise in a single step with the text prompt “Gold”. As touched upon in our interactive UMAP, Chinese characters often contain components known as radicals which can convey sound (phonetic radicals) or meaning (semantic radicals). A common semantic radical is derived from the character meaning “gold”, “金”, and is used in characters that are in some broad sense associated with gold or metals.

Even with a single sampling step, conditioning guides denoising towards the relevant regions of the probability distribution.

The figure shows that even though a single step is insufficient to approximate the denoising trajectory very well, we have moved into a region of our probability distribution with the “金” radical. This indicates that the text prompt is effectively guiding our sampling towards a region of the glyph probability distribution related to the meaning of the prompt. The animation below shows a 120 step denoising sequence for the same prompt, “Gold”. You can see that every generated glyph has either the 釒 or 钅 radical (the same radical in traditional and simplified Chinese, respectively).

Takeaway

Conditioning enables us to sample meaningful outputs from diffusion models.

Further remarks

I found that with the help of tutorials and existing libraries, it was possible to implement a working diffusion model despite not having a full understanding of what was going on under the hood. I think this is a good way to start learning and highly recommend Hugging Face’s tutorial on training a simple diffusion model using their diffusers Python library (which now includes my small bugfix!).

I’ve omitted some topics that are crucial to how production-grade diffusion models function, but are unnecessary for core understanding. One is the question of how to generate high resolution images. In our example, we did everything in pixel space, but this becomes very computationally expensive for large images. The general approach is to perform diffusion in a smaller space, then upscale it in a separate step. Methods include latent diffusion (used in Stable Diffusion) and cascaded super-resolution models (used in Imagen). Another topic is classifier-free guidance, a very elegant method for boosting the conditioning effect to give much better prompt adherence. I show the implementation in my previous post on the glyffuser and highly recommend this article if you want to learn more.

Fun extras

Diffusion sampling using the DPMSolverSDEScheduler developed by Katherine Crowson and implemented in Hugging Face diffusers—note the smooth transition from noise to data.

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Chevron Corp. intends to finance Venezuelan oil investments with cash from oil sales rather than committing new capital to the country, Chief Financial Officer Eimear Bonner said in an interview. Chevron plans to increase its Venezuelan production by 50% within the next two years but will do so without changing overall capital spending, said Bonner, who’s Chevron career has included tours of duty from Thailand and the UK to Central Asia. The Venezuelan growth plan requires additional authorizations from the US Treasury, she noted. “Our model is a venture-funded model,” Bonner said. “Any change in our investment levels or capital levels, we’d look at this like any asset opportunity or investment opportunity that we have in the portfolio. It would need to have an appropriate return on investment.” The only oil supermajor operating in Venezuela, Chevron’s cautious stance on injecting fresh capital is a reality check on how quickly the nation’s oil industry can be revived. While it has the world’s biggest reserves on paper, socialist regimes leaders have a history of nationalizing oilfields drilled by US and European operators. Chevron currently produces about 250,000 barrels a day from joint ventures with state-owned Petroleos de Venezuela SA. The country accounts for about 2% of Chevron’s annual cash flow. Bonner welcomed Acting President Delcy Rodriguez’s efforts to reform the country’s nationalist oil policies in moves that promises to lower taxes and permit more foreign investment. “It appears that those reforms are working toward ensuring all the things that would make Venezuela an attractive place for future investment: rule of law, commercial stability, competitiveness,” Bonner said. “It seems like a step in the right direction.” WHAT DO YOU THINK? Generated by readers, the comments included herein do not reflect the views and opinions of Rigzone. All comments are subject to editorial review. Off-topic, inappropriate

Oil Closes Lower but Posts Strong Monthly Gain

Oil edged lower, though still notched its biggest monthly gain since 2022, as US President Donald Trump reiterated openness to negotiations with Iran, though investors remain on edge about the potential for further tensions. West Texas Intermediate fell 0.3% to settle near $65 a barrel, snapping a breathless three-day rally, while Brent ended the day above $70. Prices tumbled after Trump told reporters that Iran wants to make a deal. The US president’s messaging has shifted from punishing Tehran for its deadly crackdown on protesters to this week trying to extract a new nuclear agreement. That siphoned some risk premium out of a market on edge after Trump ordered naval assets to the region, with an aircraft-carrier strike group recently arriving in the Middle East. The Islamic Republic is the fifth-biggest producer in the OPEC+ alliance, when including Russia. The de-escalatory remarks from Trump aren’t necessarily new, but heading into the weekend, the market is trying to gauge where Trump’s head is at, said Rebecca Babin, a senior energy trader at CIBC Private Wealth Group. “Any signal that he may lean toward diplomacy rather than military action creates immediate selling pressure,” she added. Crude had earlier fallen alongside other markets as Trump’s nomination of Kevin Warsh as the next Federal Reserve chair led to a debate about how far he would cut interest rates. The US president later said that Warsh “certainly wants to cut rates.” Several bullish factors are still at play, limiting the slide. In the US, coastal cities are bracing for a record-setting cold spell to intensify in coming days, in a potential disruption to production and boost to heating demand. The storm would come just a week after Winter Storm Fern shut in nearly 2 million barrels a day of US oil production at its peak,

Greece Warns Shipowners Against Sailing Near Iran Coast

Greece, home to the world’s largest oil tanker fleet, told the nation’s vessel owners to do what they can to stay away from Iran’s coast — a task that is all but impossible for those entering the Persian Gulf to collect cargoes of Middle East crude. Shipowners were directed to sail closer to the United Arab Emirates and Oman when transiting the Strait of Hormuz, according to two advisories seen by Bloomberg. They were issued by the Greek shipping ministry to local shipowner associations on Jan. 27 and 29. The advisories said more warships were operating near the strait and warned that the European Union’s latest sanctions on Iran risked further inflaming tensions around Hormuz, the Persian Gulf and southern parts of the Red Sea. They were sent to the Hellenic Chamber of Shipping, the Union of Greek Shipowners and the Hellenic Shortsea Shipowners Association. A spokesman for Greece’s shipping ministry confirmed the notices had been sent. The global shipping community and oil traders are closely watching developments in the Middle East after the US dispatched an aircraft-carrier strike group to the region. President Donald Trump said he hoped he would not have to use it against Iran, which monitoring groups have accused of killing thousands of people during recent protests. The Strait of Hormuz is critical to the global oil supply, with roughly a quarter of the world’s seaborne crude passing through the corridor. Much of that oil is transported on Greek-owned vessels. Greece is the biggest tanker owner by tonnage, according to Clarkson Research Services, a unit of the world’s largest shipbroker. WHAT DO YOU THINK? Generated by readers, the comments included herein do not reflect the views and opinions of Rigzone. All comments are subject to editorial review. Off-topic, inappropriate or insulting comments will be removed.

Exxon, Chevron Lift Oil Production, Blunting Price Drop

Exxon Mobil Corp. and Chevron Corp. surpassed profit expectations as higher oil production helped offset the blow from lower crude prices. The titans of the US oil industry expanded output from the US Permian Basin, Guyana and other regions. For Exxon, full-year production hit a 40-year high while Chevron benefited from the integration of its $48 billion takeover of Hess Corp. The outperformance comes as major US drillers face growing pressure to assist in the Trump administration’s aspiration to revive the Venezuelan oil sector after the ouster of strongman Nicolas Maduro. Chevron intends to finance a 50% increase in its Venezuelan oil production with cash from oil sales rather than committing new capital to the country, Chief Financial Officer Eimear Bonner said during an interview. As the only major oil explorer with ongoing operations in the South American nation, Chevron has a leg up on rivals that departed years ago during a nationalization campaign by Maduro’s predecessor, the late former leader Hugo Chavez. Late Thursday, The Trump administration took steps to begin relaxing some of the punishing sanctions that have isolated the Venezuelan energy industry. The move gives other US companies the go-ahead to work with the state-controlled oil producer, with restrictions such as a prohibition on transactions with Chinese-tied entities. Exxon’s adjusted fourth-quarter net income of $1.71 a share was 2 cents higher than the average estimate in a Bloomberg survey. Chevron earned $1.52 a share, 14 cents higher than expected. For both companies, debt ratios crept higher during the final three months of 2025. Exxon shares fell 1% at 9:35 a.m. in New York. Chevron rose 1.1%. “We’re capturing more value from every barrel and molecule we produce and building growth platforms at scale,” Chief Executive Officer Darren Woods said in a statement. The strategy is “creating a

How Robotics Is Re-Engineering Data Center Construction and Operations

Physical AI: A Reusable Robotics Stack for Data Center Operations This is where the recent collaboration between Multiply Labs and NVIDIA becomes relevant, even though the application is biomanufacturing rather than data centers. Multiply Labs has outlined a robotics approach built on three core elements: Digital twins using NVIDIA Isaac Sim to model hardware and validate changes in simulation before deployment. Foundation-model-based skill learning via NVIDIA Isaac GR00T, enabling robots to generalize tasks rather than rely on brittle, hard-coded behaviors. Perception pipelines including FoundationPose and FoundationStereo, that convert expert demonstrations into structured training data. Taken together, this represents a reusable blueprint for data center robotics. Applying the Lesson to Data Center Environments The same physical-AI techniques now being applied in lab and manufacturing environments map cleanly onto the realities of data center operations, particularly where safety, uptime, and variability intersect. Digital-twin-first deployment Before a robot ever enters a live data hall, it needs to be trained in simulation. That means modeling aisle geometry, obstacles, rack layouts, reflective surfaces, and lighting variation; along with “what if” scenarios such as blocked aisles, emergency egress conditions, ladders left in place, or spill events. Simulation-first workflows make it possible to validate behavior and edge cases before introducing any new system into a production environment. Skill learning beats hard-coded rules Data centers appear structured, but in practice they are full of variability: temporary cabling, staged parts, mixed-vendor racks, and countless human exceptions. Foundation-model approaches to manipulation are designed to generalize across that messiness far better than traditional rule-based automation, which tends to break when conditions drift even slightly from the expected state. Imitation learning captures tribal knowledge Many operational tasks rely on tacit expertise developed over years in the field, such as how to manage stiff patch cords, visually confirm latch engagement, or stage a

Applied Digital CEO Wes Cummins On the Hard Part of the AI Boom: Execution

Designing for What Comes After the Current AI Cycle Applied Digital’s design philosophy starts with a premise many developers still resist: today’s density assumptions may not hold. “We’re designing for maximum flexibility for the future—higher density power, lower density power, higher voltage delivery, and more floor space,” Cummins said. “It’s counterintuitive because densities are going up, but we don’t know what comes next.” That choice – to allocate more floor space even as rack densities climb – signals a long-view approach. Facilities are engineered to accommodate shifts in voltage, cooling topology, and customer requirements without forcing wholesale retrofits. Higher-voltage delivery, mixed cooling configurations, and adaptable data halls are baked in from the start. The goal is not to predict the future perfectly, Cummins stressed, but to avoid painting infrastructure into a corner. Supply Chain as Competitive Advantage If flexibility is the design thesis, supply chain control is the execution weapon. “It’s a huge advantage that we locked in our MEP supply chain 18 to 24 months ago,” Cummins said. “It’s a tight environment, and more timelines are going to get missed in 2026 because of it.” Applied Digital moved early to secure long-lead mechanical, electrical, and plumbing components; well before demand pressure fully rippled through transformers, switchgear, chillers, generators, and breakers. That foresight now underpins the company’s ability to make credible delivery commitments while competitors confront procurement bottlenecks. Cummins was blunt: many delays won’t stem from poor planning, but from simple unavailability. From 100 MW to 700 MW Without Losing Control The past year marked a structural pivot for Applied Digital. What began as a single, 100-megawatt “field of dreams” facility in North Dakota has become more than 700 MW under construction, with expansion still ahead. “A hundred megawatts used to be considered scale,” Cummins said. “Now we’re at 700

From Silicon to Cooling: Dell’Oro Maps the AI Data Center Buildout

For much of the past decade, data center growth could be measured in incremental gains: another efficiency point here, another capacity tranche there. That era is over. According to a cascade of recent research from Dell’Oro Group, the AI investment cycle has crossed into a new phase, one defined less by experimentation and more by industrial-scale execution. Across servers, networks, power, and cooling, Dell’Oro’s latest data points to a market being reshaped end-to-end by AI workloads which are pulling forward capital spending, redefining bill-of-material assumptions, and forcing architectural transitions that are rapidly becoming non-negotiable. Capex Becomes the Signal The clearest indicator of the shift is spending. Dell’Oro reported that worldwide data center capital expenditures rose 59 percent year-over-year in 3Q 2025, marking the eighth consecutive quarter of double-digit growth. Importantly, this is no longer a narrow, training-centric surge. “The Top 4 US cloud service providers—Amazon, Google, Meta, and Microsoft—continue to raise data center capex expectations for 2025, supported by increased investments in both AI and general-purpose infrastructure,” said Baron Fung, Senior Research Director at Dell’Oro Group. He added that Oracle is on track to double its data center capex as it expands capacity for the Stargate project. “What is notable this cycle is not just the pace of spending, but the expanding scope of investment,” Fung said. Hyperscalers are now scaling accelerated compute, general-purpose servers, and the supporting infrastructure required to deploy AI at production scale, while simultaneously applying tighter discipline around asset lifecycles and depreciation to preserve cash flow. The result is a capex environment that looks less speculative and more structural, with investment signals extending well into 2026. Accelerators Redefine the Hardware Stack At the component level, the AI effect is even more pronounced. Dell’Oro found that global data center server and storage component revenue jumped 40 percent

Rethinking Water in the AI Data Center Era

Finding Water by Eliminating Waste: Leakage as a Hidden Demand Driver ION Water and Meta frame leakage not as a marginal efficiency issue, but as one of the largest and least visible sources of water demand. According to the release, more than half of the water paid for at some properties can be lost to “invisible leaks,” including running toilets, aging water heaters, and faulty fixtures that go undetected for extended periods. ION’s platform is designed to surface that hidden demand. By monitoring water consumption at the unit level, the system flags anomalies in real time and directs maintenance teams to specific fixtures, rather than entire buildings. The company says this approach can reduce leak-driven water waste by as much as 60%. This represents an important evolution in how hyperscalers defend and contextualize their water footprints: Instead of focusing solely on their own direct WUE metrics, operators are investing in demand reduction within the same watershed where their data centers operate. That shift reframes the narrative from simply managing active water consumption to actively helping stabilize stressed local water systems. The Accounting Shift: Volumetric Water Benefits (VWB) The release explicitly positions the project as a model for Volumetric Water Benefits (VWB) initiatives, projects intended to deliver measurable environmental gains while also producing operational and financial benefits for underserved communities. This framing aligns with a broader stewardship accounting movement promoted by organizations such as the World Resources Institute, which has developed Volumetric Water Benefit Accounting (VWBA) as a standardized method for quantifying and valuing watershed-scale benefits. Meta is explicit that the project supports its water-positive commitment tied to its Temple, Texas data center community. The company has set a 2030 goal to restore more water than it consumes across its global operations and has increasingly emphasized “water stewardship in our data center

Microsoft and Meta’s Earnings Week Put the AI Data Center Cycle in Sharp Relief

If you’re trying to understand where the hyperscalers really are in the AI buildout, beyond the glossy campus renders and “superintelligence” rhetoric, this week’s earnings calls from Microsoft and Meta offered a more grounded view. Both companies are spending at a scale the data center industry has never had to absorb at once. Both are navigating the same hard constraints: power, capacity, supply chain, silicon allocation, and time-to-build. But the market’s reaction split decisively, and that divergence tells its own story about what investors will tolerate in 2026. To wit: Massive capex is acceptable when the return narrative is already visible in the P&L…and far less so when the payoff is still being described as “early innings.” Microsoft: AI Demand Is Real. So Is the Cost Microsoft’s fiscal Q2 2026 results reinforced the core fact that has been driving North American hyperscale development for two years: Cloud + AI growth is still accelerating, and Azure remains one of the primary runways. Microsoft said Q2 total revenue rose to $81.3 billion, while Microsoft Cloud revenue reached $51.5 billion, up 26% (constant currency 24%). Intelligent Cloud revenue hit $32.9 billion, up 29%, and Azure and other cloud services revenue grew 39%. That’s the demand signal. The supply signal is more complicated. On the call and in follow-on reporting, Microsoft’s leadership framed the moment as a deliberate capacity build into persistent AI adoption. Yet the bill for that build is now impossible to ignore: Reuters reported Microsoft’s capital spending totaled $37.5 billion in the quarter, up nearly 66% year-over-year, with roughly two-thirds going toward computing chips. That “chips first” allocation matters for the data center ecosystem. It implies a procurement and deployment reality that many developers and colo operators have been living: the short pole is not only power and buildings; it’s GPU

Network engineers take on NetDevOps roles to advance stalled automation efforts

What NetDevOps looks like Most enterprises begin their NetDevOps journey modestly by automating a limited set of repetitive, lower-level tasks. Nearly 70% of enterprises pursuing infrastructure automation start with task-level scripting, rather than end-to-end automation, according to theCUBE Research’s AppDev Done Right Summit. This can include using tools such as Ansible or Python scripts to standardize device provisioning, configuration changes, or other routine changes. Then, more mature teams adopt Git for version control, define golden configurations, and apply basic validation before and after changes, explains Bob Laliberte, principal analyst at SiliconANGLE and theCUBE. A smaller group of enterprises extends automation efforts into complete CI/CD-style workflows with consistent testing, staged deployments, and automated verification, Laliberte adds. This capability is present in less than 25% of enterprises today, according to theCUBE, and it is typically focused on specific domains such as data center fabric or cloud networking. NetDevOps usually exists with the network organization as a dedicated automation or platform subgroup, and more than 60% of enterprises anchor NetDevOps initiatives within traditional infrastructure teams rather than application or platform engineering groups, according to Laliberte. “In larger enterprises, NetDevOps capabilities are increasingly centralized within shared infrastructure or platform teams that provide tooling, pipelines, and guardrails across compute, storage, and networking,” Laliberte says. “In more advanced or cloud-native environments, network specialists may be embedded within application, site reliability engineering (SRE), or platform teams, particularly where networking directly impacts application performance.” Transforming work At its core, NetDevOps isn’t just about changing titles for network engineers. It is about changing workflows, behaviors, and operating models across network operations.

Microsoft will invest $80B in AI data centers in fiscal 2025

And Microsoft isn’t the only one that is ramping up its investments into AI-enabled data centers. Rival cloud service providers are all investing in either upgrading or opening new data centers to capture a larger chunk of business from developers and users of large language models (LLMs). In a report published in October 2024, Bloomberg Intelligence estimated that demand for generative AI would push Microsoft, AWS, Google, Oracle, Meta, and Apple would between them devote $200 billion to capex in 2025, up from $110 billion in 2023. Microsoft is one of the biggest spenders, followed closely by Google and AWS, Bloomberg Intelligence said. Its estimate of Microsoft’s capital spending on AI, at $62.4 billion for calendar 2025, is lower than Smith’s claim that the company will invest $80 billion in the fiscal year to June 30, 2025. Both figures, though, are way higher than Microsoft’s 2020 capital expenditure of “just” $17.6 billion. The majority of the increased spending is tied to cloud services and the expansion of AI infrastructure needed to provide compute capacity for OpenAI workloads. Separately, last October Amazon CEO Andy Jassy said his company planned total capex spend of $75 billion in 2024 and even more in 2025, with much of it going to AWS, its cloud computing division.

John Deere unveils more autonomous farm machines to address skill labor shortage

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More Self-driving tractors might be the path to self-driving cars. John Deere has revealed a new line of autonomous machines and tech across agriculture, construction and commercial landscaping. The Moline, Illinois-based John Deere has been in business for 187 years, yet it’s been a regular as a non-tech company showing off technology at the big tech trade show in Las Vegas and is back at CES 2025 with more autonomous tractors and other vehicles. This is not something we usually cover, but John Deere has a lot of data that is interesting in the big picture of tech. The message from the company is that there aren’t enough skilled farm laborers to do the work that its customers need. It’s been a challenge for most of the last two decades, said Jahmy Hindman, CTO at John Deere, in a briefing. Much of the tech will come this fall and after that. He noted that the average farmer in the U.S. is over 58 and works 12 to 18 hours a day to grow food for us. And he said the American Farm Bureau Federation estimates there are roughly 2.4 million farm jobs that need to be filled annually; and the agricultural work force continues to shrink. (This is my hint to the anti-immigration crowd). John Deere’s autonomous 9RX Tractor. Farmers can oversee it using an app. While each of these industries experiences their own set of challenges, a commonality across all is skilled labor availability. In construction, about 80% percent of contractors struggle to find skilled labor. And in commercial landscaping, 86% of landscaping business owners can’t find labor to fill open positions, he said. “They have to figure out how to do

2025 playbook for enterprise AI success, from agents to evals

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More 2025 is poised to be a pivotal year for enterprise AI. The past year has seen rapid innovation, and this year will see the same. This has made it more critical than ever to revisit your AI strategy to stay competitive and create value for your customers. From scaling AI agents to optimizing costs, here are the five critical areas enterprises should prioritize for their AI strategy this year. 1. Agents: the next generation of automation AI agents are no longer theoretical. In 2025, they’re indispensable tools for enterprises looking to streamline operations and enhance customer interactions. Unlike traditional software, agents powered by large language models (LLMs) can make nuanced decisions, navigate complex multi-step tasks, and integrate seamlessly with tools and APIs. At the start of 2024, agents were not ready for prime time, making frustrating mistakes like hallucinating URLs. They started getting better as frontier large language models themselves improved. “Let me put it this way,” said Sam Witteveen, cofounder of Red Dragon, a company that develops agents for companies, and that recently reviewed the 48 agents it built last year. “Interestingly, the ones that we built at the start of the year, a lot of those worked way better at the end of the year just because the models got better.” Witteveen shared this in the video podcast we filmed to discuss these five big trends in detail. Models are getting better and hallucinating less, and they’re also being trained to do agentic tasks. Another feature that the model providers are researching is a way to use the LLM as a judge, and as models get cheaper (something we’ll cover below), companies can use three or more models to

OpenAI’s red teaming innovations define new essentials for security leaders in the AI era

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More OpenAI has taken a more aggressive approach to red teaming than its AI competitors, demonstrating its security teams’ advanced capabilities in two areas: multi-step reinforcement and external red teaming. OpenAI recently released two papers that set a new competitive standard for improving the quality, reliability and safety of AI models in these two techniques and more. The first paper, “OpenAI’s Approach to External Red Teaming for AI Models and Systems,” reports that specialized teams outside the company have proven effective in uncovering vulnerabilities that might otherwise have made it into a released model because in-house testing techniques may have missed them. In the second paper, “Diverse and Effective Red Teaming with Auto-Generated Rewards and Multi-Step Reinforcement Learning,” OpenAI introduces an automated framework that relies on iterative reinforcement learning to generate a broad spectrum of novel, wide-ranging attacks. Going all-in on red teaming pays practical, competitive dividends It’s encouraging to see competitive intensity in red teaming growing among AI companies. When Anthropic released its AI red team guidelines in June of last year, it joined AI providers including Google, Microsoft, Nvidia, OpenAI, and even the U.S.’s National Institute of Standards and Technology (NIST), which all had released red teaming frameworks. Investing heavily in red teaming yields tangible benefits for security leaders in any organization. OpenAI’s paper on external red teaming provides a detailed analysis of how the company strives to create specialized external teams that include cybersecurity and subject matter experts. The goal is to see if knowledgeable external teams can defeat models’ security perimeters and find gaps in their security, biases and controls that prompt-based testing couldn’t find. What makes OpenAI’s recent papers noteworthy is how well they define using human-in-the-middle

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