It's too easy and too common for experts and casual observers alike to discuss bond markets through the lens of inflation. It's easy and common because inflation is always a consideration for bonds. To understand exactly why this is, consider an example where you give me $100 today and I agree to pay you 11 payments of $10 dollars this year. That's a 10% return in dollars, but it's only a 10% return in value if there's no inflation. For instance, if the $110 you'll ultimately get back would buy a new pair of shoes today, if inflation rises, those same shoes might cost $140 next year. So you're $10 return would be more like a $30 loss if inflation were completely out of control.
Those numbers aren't realistic when it comes to overall inflation metrics, but it helps illustrate the point. All other things being equal, bond yields are generally higher than inflation, because absent artificial boosts (like Fed buying), investors wouldn't make money if yields were lower than inflation.
TIPS (Treasury inflation-protected securities) offer investors a Treasury yield that's protected from inflation fluctuations (based on the mainstream inflation reported via CPI). This lets us see the "non-inflation-related component" of 10yr yields. Subtracting that from the 10yr yields leaves us with implied inflation expectations. All of the above can be seen in the chart below (expressed in "change from 1/1/2018").
Bottom line, inflation isn't helping, but the non-inflation-related component is doing much more damage--especially recently. This has to do with factors like growth, monetary policy (i.e. Fed hikes and bond-buying plans), and fiscal policy (i.e. more Treasury supply/issuance to pay for stuff like the tax bill and infrastructure plans).
In the bigger picture, bonds remain in bad shape as the yield curve is making a serious move back toward higher/steeper levels. That means 10 and 2yr yields are getting farther apart after massive amounts of tightening in recent years. There's likely a limit as to how much the curve will re-steepen (2yr yields aren't likely to fall and 10yr yields can only go so high before doing damage to the economy), but until that limit is realized, the steepening trade will continue adding to outright weakness in longer-term bonds like 10yr Treasuries and MBS.