One research group examined the effects of the AIP on IBD disease activity, quality of life, and gene expression (which measures the extent to which a cell is using information in its DNA to carry out certain processes) in the inner lining of the intestines. In that open-label, uncontrolled study, 18 adults with active ulcerative colitis or Crohn’s disease followed a 6-week elimination phase and subsequent 5-week maintenance phase (but no foods were reintroduced).
Out of the 14 participants who completed the intervention, 11 achieved clinical remission by the sixth week and sustained it through the maintenance phase. Though C-reactive protein (a marker of inflammation) and faecal calprotectin (a marker of intestinal damage) were elevated in some participants at the beginning of the study and lower after the intervention, those changes were not statistically significant. Two participants experienced worsening symptoms, and only about two-thirds of the participants actually adhered to the diet. 
Participants also completed quality-of-life questionnaires every 2 weeks, from baseline to the final week, but survey responses dwindled rapidly from 13 participants at baseline to only 4 at weeks 9 and 11. Average quality-of-life scores increased, and participants reported improvements in bowel movement frequency, stress, and ability to perform leisure activities. 
Researchers also measured gene expression in the mucosal lining of the intestines and found that some genes increased or decreased compared with baseline numbers. They interpreted this as a potential sign of mucosal healing, but it wasn’t explored further.
In an open-label, uncontrolled pilot study, 17 women with Hashimoto’s thyroiditis participated in a 10-week online coaching program on the AIP diet. Quality of life, clinical symptom burden (both the severity of symptoms and the perceived impact on the client’s life), and blood markers were assessed at baseline and after the intervention. Quality of life and symptom scores improved. C-reactive protein values and white blood cell count were lower after the intervention, but they were always within normal ranges. Although no markers of thyroid function or thyroid antibodies changed over the course of the program, 6 of the 13 women who had been using a thyroid medication reduced their dose after the program. Weight and body mass index (BMI) were significantly lower after the study, but based on the lack of change in thyroid markers, it’s unlikely that this was caused by a change in thyroid function. Notably, in their conflict of interest statement, the authors disclosed that they are the co-founders of the company that provided coaching for the participants in this study. 
Limited, low quality evidence suggests that quality of life and IBD disease activity may improve on the AIP, but it doesn't affect markers of thyroid function.
Any dietary change can potentially affect the gut microbiome, but no studies have explored the effects of the AIP diet on it. Evidence in humans is limited, but recent studies have shown that fermented foods may alter the microbiome. Stronger evidence indicates that Mediterranean diets — rich in fruits, vegetables, legumes, nuts, grains, and plant-based oils — are associated with unique microbiome characteristics and protection against some diseases. The AIP shares some characteristics with Mediterranean diets, but research is needed to determine whether the AIP might modify the microbiome in similar ways.
The Dietary Inflammatory Index (DII) is a relatively new tool used to assess the inflammatory potential of dietary patterns, based on findings from about 2,000 articles that studied the relationship between diets and inflammatory markers. Forty-five specific “food parameters” have been identified and assigned an “inflammatory weight,” which reflects their influence on six markers of inflammation. Although some specific foods and drinks, such as garlic, onion, and alcohol, are included, many of the parameters are vitamins and compounds found in plants.
While one food in isolation may not exert a strong pro- or anti-inflammatory effect, certain dietary patterns are associated with higher or lower levels of inflammatory markers. Dietary patterns with a high index score are associated with an increased risk of depression, certain cancers, and mortality from cardiovascular disease; those with low scores appear protective, but the reason is still unknown. 
The Gut and Psychology Syndrome (GAPS), Specific Carbohydrate (SCD), and low-FODMAP (fermentable oligosaccharides, disaccharides, monosaccharides, and polyols) diets are all elimination diets. Each was developed based on different theories and is supported by varying levels of evidence.
The most evidence-based diet of the three is the low-FODMAP diet, which temporarily reduces certain foods with sugars that are thought to contribute to gastrointestinal (GI) distress by retaining water in the intestines or undergoing microbial fermentation. After the initial elimination phase, these groups of carbohydrates are systematically reintroduced to test for an individual’s tolerance level. Researchers developed the low-FODMAP diet after discovering that these sugars increased the fluid content of feces and were also rapidly fermented by gut microbes, leading to gas production. In people with irritable bowel syndrome (IBS), the sugars can lead to severe GI distress, and the process of elimination, testing, and reintroduction at personally tolerable levels improves symptoms in up to 70% of people.
Natasha Campbell-McBride, MD, MMedSci (in neurology and nutrition) developed the GAPS diet to treat her son’s autism. Her GAPS diet — like the SCD and AIP — points to malnutrition, dysbiosis, and “leaky gut” as the causes of diseases and mood disorders. The diet consists of an optional introductory phase, followed by the full GAPS elimination diet and then subsequent reintroduction phase. Foods allowed on the diet include eggs, meat, fresh fruits and vegetables, nuts, unprocessed fats, and garlic. Eating fermented foods and bone broth at every meal is also recommended, as is buying organic food, avoiding processed foods, and combining specific foods. Despite anecdotal reports of improvement on the diet, it has never been formally researched, and some of the theories have been either unsubstantiated or debunked.
The SCD is an elimination diet that was developed in the early 1900s to treat celiac disease. It was based on the theory that people with celiac could not tolerate certain sugars (not gluten), so it consisted primarily of ripe bananas and calcium caseinate until bowel habits improved, and then foods were gradually reintroduced.  The diet was repopularized in the 1990s by a biochemist who claimed it could cure celiac, IBD, diverticulitis, and autism spectrum disorder. However, these claims have not been substantiated.  Limited, low-quality evidence suggests that the SCD improves symptoms of Crohn’s disease as effectively as a Mediterranean or whole-foods diet, but since participants knew about their dietary changes and none of these studies included a control group, the results could have been influenced by the placebo effect and other changes associated with a new diet.
The AIP, GAPS, SCD, and low-FODMAP diets are all examples of elimination diets intended to reduce the symptoms of GI or autoimmune diseases. The low-FODMAP diet is the most evidence-based of the diets.